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Juisheng Chen - One of the best experts on this subject based on the ideXlab platform.
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analytical Power Series Solution for contaminant transport with hyperbolic asymptotic distance dependent dispersivity
Journal of Hydrology, 2008Co-Authors: Juisheng Chen, Chingping Liang, Chenchung ChiangAbstract:Summary A hyperbolic asymptotic function, which characterizes that the dispersivity initially increases with travel distance and eventually reaches an asymptotic value at long travel distance, is adopted and incorporated into the general advection–dispersion equation for describing scale-dependent solute transport in porous media in this study. An analytical technique for solving advection–dispersion equation with hyperbolic asymptotic distance-dependent dispersivity is presented. The analytical Solution is derived by applying the extended Power Series method coupling with the Laplace transform. The developed analytical Solution is compared with the corresponding numerical Solution to evaluate its accuracy. Results demonstrate that the breakthrough curves at different locations obtained from the derived Power Series Solution agree closely with those from the numerical Solution. Moreover, breakthrough curves obtained from the hyperbolic asymptotic dispersivity model are compared with those obtained from the constant dispersivity model to scrutinize the relationship of the transport parameters derived by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47]. The result reveals that the relationship postulated by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47] is only valid under conditions with small dimensionless asymptotic dispersivity (aa) and large dimensionless characteristic half length (b).
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two dimensional Power Series Solution for non axisymmetrical transport in a radially convergent tracer test with scale dependent dispersion
Advances in Water Resources, 2007Co-Authors: Juisheng ChenAbstract:Abstract It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical Solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The Power Series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical Solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the Power Series Solution and the numerical Solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed Power Series Solution facilitates fast prediction of the breakthrough curves at any observation point.
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two dimensional laplace transformed Power Series Solution for solute transport in a radially convergent flow field
Advances in Water Resources, 2003Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:This paper presents an analytical Solution for two-dimensional non-axisymmetric solute transport in a radially convergent flow field. We applied a Laplace-transformed Power Series (LTPS) technique to solve the two-dimensional advection-dispersion equation in cylindrical coordinates. The Solution is compared with a numerical Solution to evaluate its robustness and accuracy. The applicable Peclet number range of the developed Power Series Solution is also examined. Results show that the LTPS technique can effectively and accurately handle the two-dimensional radial advection-dispersion equation for a Peclet number up to 60. The two-dimensional Power Series Solution is appropriate for hydrogeologic circumstances where temporally and spatially continuous Solutions are demanded.
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a laplace transform Power Series Solution for solute transport in a convergent flow field with scale dependent dispersion
Water Resources Research, 2003Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:[1] This study presents a novel mathematical model to describe solute transport in a radially convergent flow field with scale-dependent dispersion. The scale-dependent advection-dispersion equation in cylindrical coordinates derived based on the dispersivity is assumed to increase linearly with the distance of the solute transported from its input source. The Laplace transformed Power Series technique is applied to solve the radially scale-dependent advection-dispersion equation with variable coefficients. Breakthrough curves obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model to illustrate the features of scale-dependent dispersion in a radially convergent flow field. The comparison results reveal that the constant dispersivity model can produce a type curve with the same shape as that from the proposed scale-dependent dispersivity model. This correspondence in type curves between the two models occurs when the product of the Peclet number used in the constant dispersivity model and the dispersivity/distance ratio used in the scale-dependent dispersivity model equals 4. Finally, the scale-dependent dispersivity model is applied to a set of previously reported field data to investigate the linearly scale-dependent dispersion effect. The analytical results reveal that the linearly scale-dependent dispersion model is applicable to this test site.
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a novel analytical Power Series Solution for solute transport in a radially convergent flow field
Journal of Hydrology, 2002Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:The concentration breakthrough curves at a pumping well for solute transport in a radially convergent flow field are governed by an advective ‐ dispersive second order partial differential equation with a radial distance-dependent velocity and dispersion coefficient. The Laplace transform is generally first employed to eliminate the temporal derivative to solve the partial differential equation. The Laplace transformed equations are then converted to the standard form of the special Airy function through successive applications of variable change. This study presents the Solution of the Laplace-transformed equation without using the special Airy function. A direct Power Series method and a Power Series method with variable changes to eliminate the advection term that usually results in numerical errors for large Peclet numbers are applied to obtain an analytical Solution in the Laplace domain. The obtained Solutions are compared to other Airy function-formed Solutions to examine the method’s robustness and accuracy. Analytical results indicate that the Laplace transform Power Series method with variable change can effectively and accurately handle the radial advection ‐ dispersion equation of high Peclet numbers, whereas the direct Power Series method can only evaluate the Solution for medium Peclet numbers. The novel Power Series technique with variable change is valuable for future quantitative hydrogeological issues with variable dependent differential equation and can be extended to higher dimensional problems. q 2002 Elsevier Science B.V. All rights reserved.
Chungmin Liao - One of the best experts on this subject based on the ideXlab platform.
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two dimensional laplace transformed Power Series Solution for solute transport in a radially convergent flow field
Advances in Water Resources, 2003Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:This paper presents an analytical Solution for two-dimensional non-axisymmetric solute transport in a radially convergent flow field. We applied a Laplace-transformed Power Series (LTPS) technique to solve the two-dimensional advection-dispersion equation in cylindrical coordinates. The Solution is compared with a numerical Solution to evaluate its robustness and accuracy. The applicable Peclet number range of the developed Power Series Solution is also examined. Results show that the LTPS technique can effectively and accurately handle the two-dimensional radial advection-dispersion equation for a Peclet number up to 60. The two-dimensional Power Series Solution is appropriate for hydrogeologic circumstances where temporally and spatially continuous Solutions are demanded.
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a laplace transform Power Series Solution for solute transport in a convergent flow field with scale dependent dispersion
Water Resources Research, 2003Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:[1] This study presents a novel mathematical model to describe solute transport in a radially convergent flow field with scale-dependent dispersion. The scale-dependent advection-dispersion equation in cylindrical coordinates derived based on the dispersivity is assumed to increase linearly with the distance of the solute transported from its input source. The Laplace transformed Power Series technique is applied to solve the radially scale-dependent advection-dispersion equation with variable coefficients. Breakthrough curves obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model to illustrate the features of scale-dependent dispersion in a radially convergent flow field. The comparison results reveal that the constant dispersivity model can produce a type curve with the same shape as that from the proposed scale-dependent dispersivity model. This correspondence in type curves between the two models occurs when the product of the Peclet number used in the constant dispersivity model and the dispersivity/distance ratio used in the scale-dependent dispersivity model equals 4. Finally, the scale-dependent dispersivity model is applied to a set of previously reported field data to investigate the linearly scale-dependent dispersion effect. The analytical results reveal that the linearly scale-dependent dispersion model is applicable to this test site.
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a novel analytical Power Series Solution for solute transport in a radially convergent flow field
Journal of Hydrology, 2002Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:The concentration breakthrough curves at a pumping well for solute transport in a radially convergent flow field are governed by an advective ‐ dispersive second order partial differential equation with a radial distance-dependent velocity and dispersion coefficient. The Laplace transform is generally first employed to eliminate the temporal derivative to solve the partial differential equation. The Laplace transformed equations are then converted to the standard form of the special Airy function through successive applications of variable change. This study presents the Solution of the Laplace-transformed equation without using the special Airy function. A direct Power Series method and a Power Series method with variable changes to eliminate the advection term that usually results in numerical errors for large Peclet numbers are applied to obtain an analytical Solution in the Laplace domain. The obtained Solutions are compared to other Airy function-formed Solutions to examine the method’s robustness and accuracy. Analytical results indicate that the Laplace transform Power Series method with variable change can effectively and accurately handle the radial advection ‐ dispersion equation of high Peclet numbers, whereas the direct Power Series method can only evaluate the Solution for medium Peclet numbers. The novel Power Series technique with variable change is valuable for future quantitative hydrogeological issues with variable dependent differential equation and can be extended to higher dimensional problems. q 2002 Elsevier Science B.V. All rights reserved.
Jornet-sanz Marc - One of the best experts on this subject based on the ideXlab platform.
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Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties
'Informa UK Limited', 2020Co-Authors: Calatayud-gregori Julia, Cortés J.-c., Jornet-sanz MarcAbstract:[EN] In this work, we study the full randomized versions of Airy, Hermite and Laguerre differential equations, which depend on a random variable appearing as an equation coefficient as well as two random initial conditions. In previous contributions, the mean square stochastic Solutions to the aforementioned random differential equations were constructed via the Frobenius method, under the assumption of exponential growth of the absolute moments of the equation coefficient, which is equivalent to its essential boundedness. In this paper we aim at relaxing the boundedness hypothesis to allow more general probability distributions for the equation coefficient. We prove that the equations are solvable in the mean square sense when the equation coefficient has finite moment-generating function in a neighborhood of the origin. A thorough discussion of the new hypotheses is included.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P.Calatayud Gregori, J.; Cortés, J.; Jornet Sanz, M. (2020). Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties. Stochastic Analysis and Applications. 38(5):875-885. https://doi.org/10.1080/07362994.2020.1733017S875885385Neckel, T., & Rupp, F. (2013). Random Differential Equations in Scientific Computing. doi:10.2478/9788376560267Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Cortés, J.-C., Jódar, L., Camacho, F., & Villafuerte, L. (2010). Random Airy type differential equations: Mean square exact and numerical Solutions. Computers & Mathematics with Applications, 60(5), 1237-1244. doi:10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.-C., & Jódar, L. (2011). Random Hermite differential equations: Mean square Power Series Solutions and statistical properties. Applied Mathematics and Computation, 218(7), 3654-3666. doi:10.1016/j.amc.2011.09.008Calatayud, J., Cortés, J.-C., & Jornet, M. (2019). Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation. Mediterranean Journal of Mathematics, 16(3). doi:10.1007/s00009-019-1338-6Calatayud, J., Cortés, J.-C., Jornet, M., & Villafuerte, L. (2018). Random non-autonomous second order linear differential equations: mean square analytic Solutions and their statistical properties. Advances in Difference Equations, 2018(1). doi:10.1186/s13662-018-1848-8Gregori, J., López, J., & Sanz, M. (2018). Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling. Mathematical and Computational Applications, 23(4), 76. doi:10.3390/mca23040076Calbo, G., Cortés, J.-C., & Jódar, L. (2010). Mean square Power Series Solution of random linear differential equations. Computers & Mathematics with Applications, 59(1), 559-572. doi:10.1016/j.camwa.2009.06.007Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2010). Analytic stochastic process Solutions of second-order random differential equations. Applied Mathematics Letters, 23(12), 1421-1424. doi:10.1016/j.aml.2010.07.011CALBO SANJUÁN, G. (s. f.). Mean Square Analytic Solutions of Random Linear Models. doi:10.4995/thesis/10251/8721Jagadeesan, M. (2017). Simple analysis of sparse, sign-consistent JL. arXiv:1708.02966.Lin, G. D. (2017). Recent developments on the moment problem. Journal of Statistical Distributions and Applications, 4(1). doi:10.1186/s40488-017-0059-2Ernst, O. G., Mugler, A., Starkloff, H.-J., & Ullmann, E. (2011). On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 317-339. doi:10.1051/m2an/2011045Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square Power Series Solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.04
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On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random Power Series Solution and approximation of its statistical moments
'Wiley', 2019Co-Authors: Calatayud-gregori Julia, Cortés J.-c., Jornet-sanz MarcAbstract:"This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random Power Series Solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random Power Series around the regular¿singular point 1. A theorem on the existence and uniqueness of Lp(omega) Solution to the random Legendre differential equation on the intervals (-1,1) and (1,3) is obtained. The hypotheses assumed are simple: initial conditions in Lp(omega) and random input A in L infinite(omega) (this is equivalent to A having absolute moments that grow at most exponentially). Thus, this paper extends the deterministic theory to a random framework. Uncertainty quantification for the Solution stochastic process is performed by truncating the random Series and taking limits in Lp(omega). In the numerical experiments, we approximate its expectation and variance for certain forms of the differential equation. The reliability of our approach is compared with Monte Carlo simulations and generalized polynomial chaos expansions.Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de ValènciaCalatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random Power Series Solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045S1121
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Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation
'Springer Science and Business Media LLC', 2019Co-Authors: Calatayud-gregori Julia, Cortés J.-c., Jornet-sanz MarcAbstract:[EN] In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X-0 and X-1. In a previous study (Calbo et al. in Comput Math Appl 61(9):2782-2792, 2011), a mean square convergent Power Series Solution on (-1/e, 1/e) was constructed, under the assumptions of mean fourth integrability of X-0 and X-1, independence, and at most exponential growth of the absolute moments of A. In this paper, we relax these conditions to construct an L-p Solution (1
J C Cortes - One of the best experts on this subject based on the ideXlab platform.
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on the legendre differential equation with uncertainties at the regular singular point 1 lp ω random Power Series Solution and approximation of its statistical moments
Computational and Mathematical Methods, 2019Co-Authors: Julia Calatayud, J C Cortes, Marc JornetAbstract:"This is the peer reviewed version of the following article: Calatayud, J, Cortes, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random Power Series Solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."
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random fractional generalized airy differential equations a probabilistic analysis using mean square calculus
Applied Mathematics and Computation, 2019Co-Authors: Clara Burgos, J C Cortes, L Villafuerte, Amar Debbouche, R J VillanuevaAbstract:Abstract The aim of this paper is to study a generalization of fractional Airy differential equations whose input data (coefficient and initial conditions) are random variables. Under appropriate hypotheses assumed upon the input data, we construct a random generalized Power Series Solution of the problem and then we prove its convergence in the mean square stochastic sense. Afterwards, we provide reliable explicit approximations for the main statistical information of the Solution process (mean, variance and covariance). Further, we show a set of numerical examples where our obtained theory is illustrated. More precisely, we show that our results for the random fractional Airy equation are in full agreement with the corresponding to classical random Airy differential equation available in the extant literature. Finally, we illustrate how to construct reliable approximations of the probability density function of the Solution stochastic process to the random fractional Airy differential equation by combining the knowledge of the mean and the variance and the Principle of Maximum Entropy.
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improving the approximation of the first and second order statistics of the response process to the random legendre differential equation
arXiv: Numerical Analysis, 2018Co-Authors: Julia Calatayud, J C Cortes, Marc JornetAbstract:In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient $A$ and initial conditions $X_0$ and $X_1$. In a previous study [Calbo G. et al, Comput. Math. Appl., 61(9), 2782--2792 (2011)], a mean square convergent Power Series Solution on $(-1/e,1/e)$ was constructed, under the assumptions of mean fourth integrability of $X_0$ and $X_1$, independence, and at most exponential growth of the absolute moments of $A$. In this paper, we relax these conditions to construct an $\mathrm{L}^p$ Solution ($1\leq p\leq\infty$) to the random Legendre differential equation on the whole domain $(-1,1)$, as in its deterministic counterpart. Our hypotheses assume no independence and less integrability of $X_0$ and $X_1$. Moreover, the growth condition on the moments of $A$ is characterized by the boundedness of $A$, which simplifies the proofs significantly. We also provide approximations of the expectation and variance of the response process. The numerical experiments show the wide applicability of our findings. A comparison with Monte Carlo simulations and gPC expansions is performed.
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mean square Solution of bessel differential equation with uncertainties
Journal of Computational and Applied Mathematics, 2017Co-Authors: J C Cortes, L Jodar, L VillafuerteAbstract:This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called L p -random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized Power Series Solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated Power Series Solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method.
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random hermite differential equations mean square Power Series Solutions and statistical properties
Applied Mathematics and Computation, 2011Co-Authors: Gema Calbo, J C Cortes, L JodarAbstract:Abstract This paper deals with the construction of random Power Series Solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random Power Series Solution is mean square convergent. We provide conditions in order to obtain random polynomial Solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process Solution generated by truncation of the exact Power Series Solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation.
Nathaniel S Barlow - One of the best experts on this subject based on the ideXlab platform.
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analytic Solution of the seir epidemic model via asymptotic approximant
Physica D: Nonlinear Phenomena, 2020Co-Authors: Steven J Weinstein, Morgan S Holland, Kelly E Rogers, Nathaniel S BarlowAbstract:Abstract An analytic Solution is obtained to the SEIR Epidemic Model. The Solution is created by constructing a single second-order nonlinear differential equation in ln S and analytically continuing its divergent Power Series Solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et al., 2017) in the form of a modified symmetric Pade approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.
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accurate closed form Solution of the sir epidemic model
Physica D: Nonlinear Phenomena, 2020Co-Authors: Nathaniel S Barlow, Steven J WeinsteinAbstract:An accurate closed-form Solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et al., 2017). The Solution is created by analytically continuing the divergent Power Series Solution such that it matches the long-time asymptotic behavior of the epidemic model. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.
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asymptotic approximant for the falkner skan boundary layer equation
arXiv: Computational Physics, 2019Co-Authors: Elizabeth R Belden, Steven J Weinstein, Zachary A Dickman, Alex D Archibee, Ethan Burroughs, Nathaniel S BarlowAbstract:We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accurate analytic closed-form Solutions to the Falkner-Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[-0.198837735, 1]$ are considered, and the previously established non-unique Solutions for $\beta<0$ having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the Power Series Solution to the Falkner-Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Pade approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical Solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner-Skan Solution at large distances from the wedge.
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on the summation of divergent truncated and underspecified Power Series via asymptotic approximants
Quarterly Journal of Mechanics and Applied Mathematics, 2017Co-Authors: Nathaniel S Barlow, Steven J Weinstein, Christopher R Stanton, Nicole Hill, Allyssa G CioAbstract:A compact and accurate Solution method is provided for problems whose infinite Power Series Solution diverges and/or whose Series coefficients are only known up to a finite order. The method only requires that either the Power Series Solution or some truncation of the Power Series Solution be available and that some asymptotic behavior of the Solution is known away from the Series' expansion point. Here, we formalize the method of asymptotic approximants that has found recent success in its application to thermodynamic virial Series where only a few to (at most) a dozen Series coefficients are typically known. We demonstrate how asymptotic approximants may be constructed using simple recurrence relations, obtained through the use of a few known rules of Series manipulation. The result is an approximant that bridges two asymptotic regions of the unknown exact Solution, while maintaining accuracy in-between. A general algorithm is provided to construct such approximants. To demonstrate the versatility of the method, approximants are constructed for three nonlinear problems relevant to mathematical physics: the Sakiadis boundary layer, the Blasius boundary layer, and the Flierl-Petviashvili monopole. The Power Series Solution to each of these problems is underspecified since, in the absence of numerical simulation, one lower-order coefficient is not known; consequently, higher-order coefficients that depend recursively on this coefficient are also unknown. The constructed approximants are capable of predicting this unknown coefficient as well as other important properties inherent to each problem. The approximants lead to new benchmark values for the Sakiadis boundary layer and agree with recent numerical values for properties of the Blasius boundary layer and Flierl-Petviashvili monopole.