The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Deepika Dhall - One of the best experts on this subject based on the ideXlab platform.
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high accuracy cubic Spline Approximation for two dimensional quasi linear elliptic boundary value problems
Applied Mathematical Modelling, 2013Co-Authors: R K Mohanty, M K Jain, Deepika DhallAbstract:Abstract We report a new 9 point compact discretization of order two in y - and order four in x -directions, based on cubic Spline Approximation, for the solution of two dimensional quasi-linear elliptic partial differential equations. We describe the complete derivation procedure of the method in details and also discuss how our discretization is able to handle Poisson’s equation in polar coordinates. The convergence analysis of the proposed cubic Spline Approximation for the nonlinear elliptic equation is discussed in details and we have shown under appropriate conditions the proposed method converges. Some physical examples and their numerical results are provided to justify the advantages of the proposed method.
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a cubic Spline Approximation and application of tage iterative method for the solution of two point boundary value problems with forcing function in integral form
Applied Mathematical Modelling, 2011Co-Authors: R K Mohanty, M K Jain, Deepika DhallAbstract:In this article, we report an efficient high order numerical method based on cubic Spline Approximation and application of alternating group explicit method for the solution of two point non-linear boundary value problems, whose forcing functions are in integral form, on a non-uniform mesh. The proposed method is applicable when the internal grid points of solution interval are odd in number. The proposed cubic Spline method is also applicable to integro-differential equations having singularities. Computational results are given to demonstrate the utility of the method.
James T Thorson - One of the best experts on this subject based on the ideXlab platform.
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a stepwise selected Spline Approximation to time varying parameters with application to occupancy modelling
Methods in Ecology and Evolution, 2013Co-Authors: James T Thorson, Shijie Zhou, Andre E Punt, Anthony D M SmithAbstract:Summary Many population dynamics models and common software packages, including for capture–mark–recapture, occupancy and catch-at-age models, are estimable using parameters that are either constant for all years or vary annually. We develop a Spline Approximation to time-varying parameters, which includes the constant or annually varying case as two extremes, where the Akaike Information Criterion is used to select an appropriate degree of smoothness, ranging from change in every year to no change at all. Simulation modelling is used to evaluate the performance of this method relative to constant, annually varying, or random-effect parameter estimates when applied to an occupancy model that simultaneously estimates abundance and detectability in multiple sampling strata. We also demonstrate this method by approximating time-varying abundance using 25 years of detection/non-detection data for 42 Chondrichthyes species off northern Australia. Simulation modelling indicates that the stepwise-Spline Approximation results in lower estimation errors for the proportion of abundance in each stratum, regardless of sample sizes, the underlying form for time-varying abundance and the inclusion of unmodelled process errors. Applied to the Chondrichthyes data from northern Australia, the Spline Approximation identifies temporal variability in abundance for 34 of 42 species, and an annually varying model is never selected. We recommend this stepwise-Spline Approximation in cases where a decision is necessary between constant or annually varying forms for an estimated parameter. Possible applications include occupancy, capture–mark–recapture, catch-at-age and index standardization models.
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A stepwise‐selected Spline Approximation to time‐varying parameters, with application to occupancy modelling
Methods in Ecology and Evolution, 2012Co-Authors: James T Thorson, Shijie Zhou, Andre E Punt, Anthony D M SmithAbstract:Summary Many population dynamics models and common software packages, including for capture–mark–recapture, occupancy and catch-at-age models, are estimable using parameters that are either constant for all years or vary annually. We develop a Spline Approximation to time-varying parameters, which includes the constant or annually varying case as two extremes, where the Akaike Information Criterion is used to select an appropriate degree of smoothness, ranging from change in every year to no change at all. Simulation modelling is used to evaluate the performance of this method relative to constant, annually varying, or random-effect parameter estimates when applied to an occupancy model that simultaneously estimates abundance and detectability in multiple sampling strata. We also demonstrate this method by approximating time-varying abundance using 25 years of detection/non-detection data for 42 Chondrichthyes species off northern Australia. Simulation modelling indicates that the stepwise-Spline Approximation results in lower estimation errors for the proportion of abundance in each stratum, regardless of sample sizes, the underlying form for time-varying abundance and the inclusion of unmodelled process errors. Applied to the Chondrichthyes data from northern Australia, the Spline Approximation identifies temporal variability in abundance for 34 of 42 species, and an annually varying model is never selected. We recommend this stepwise-Spline Approximation in cases where a decision is necessary between constant or annually varying forms for an estimated parameter. Possible applications include occupancy, capture–mark–recapture, catch-at-age and index standardization models.
R K Mohanty - One of the best experts on this subject based on the ideXlab platform.
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high accuracy cubic Spline Approximation for two dimensional quasi linear elliptic boundary value problems
Applied Mathematical Modelling, 2013Co-Authors: R K Mohanty, M K Jain, Deepika DhallAbstract:Abstract We report a new 9 point compact discretization of order two in y - and order four in x -directions, based on cubic Spline Approximation, for the solution of two dimensional quasi-linear elliptic partial differential equations. We describe the complete derivation procedure of the method in details and also discuss how our discretization is able to handle Poisson’s equation in polar coordinates. The convergence analysis of the proposed cubic Spline Approximation for the nonlinear elliptic equation is discussed in details and we have shown under appropriate conditions the proposed method converges. Some physical examples and their numerical results are provided to justify the advantages of the proposed method.
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a cubic Spline Approximation and application of tage iterative method for the solution of two point boundary value problems with forcing function in integral form
Applied Mathematical Modelling, 2011Co-Authors: R K Mohanty, M K Jain, Deepika DhallAbstract:In this article, we report an efficient high order numerical method based on cubic Spline Approximation and application of alternating group explicit method for the solution of two point non-linear boundary value problems, whose forcing functions are in integral form, on a non-uniform mesh. The proposed method is applicable when the internal grid points of solution interval are odd in number. The proposed cubic Spline method is also applicable to integro-differential equations having singularities. Computational results are given to demonstrate the utility of the method.
Anthony D M Smith - One of the best experts on this subject based on the ideXlab platform.
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a stepwise selected Spline Approximation to time varying parameters with application to occupancy modelling
Methods in Ecology and Evolution, 2013Co-Authors: James T Thorson, Shijie Zhou, Andre E Punt, Anthony D M SmithAbstract:Summary Many population dynamics models and common software packages, including for capture–mark–recapture, occupancy and catch-at-age models, are estimable using parameters that are either constant for all years or vary annually. We develop a Spline Approximation to time-varying parameters, which includes the constant or annually varying case as two extremes, where the Akaike Information Criterion is used to select an appropriate degree of smoothness, ranging from change in every year to no change at all. Simulation modelling is used to evaluate the performance of this method relative to constant, annually varying, or random-effect parameter estimates when applied to an occupancy model that simultaneously estimates abundance and detectability in multiple sampling strata. We also demonstrate this method by approximating time-varying abundance using 25 years of detection/non-detection data for 42 Chondrichthyes species off northern Australia. Simulation modelling indicates that the stepwise-Spline Approximation results in lower estimation errors for the proportion of abundance in each stratum, regardless of sample sizes, the underlying form for time-varying abundance and the inclusion of unmodelled process errors. Applied to the Chondrichthyes data from northern Australia, the Spline Approximation identifies temporal variability in abundance for 34 of 42 species, and an annually varying model is never selected. We recommend this stepwise-Spline Approximation in cases where a decision is necessary between constant or annually varying forms for an estimated parameter. Possible applications include occupancy, capture–mark–recapture, catch-at-age and index standardization models.
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A stepwise‐selected Spline Approximation to time‐varying parameters, with application to occupancy modelling
Methods in Ecology and Evolution, 2012Co-Authors: James T Thorson, Shijie Zhou, Andre E Punt, Anthony D M SmithAbstract:Summary Many population dynamics models and common software packages, including for capture–mark–recapture, occupancy and catch-at-age models, are estimable using parameters that are either constant for all years or vary annually. We develop a Spline Approximation to time-varying parameters, which includes the constant or annually varying case as two extremes, where the Akaike Information Criterion is used to select an appropriate degree of smoothness, ranging from change in every year to no change at all. Simulation modelling is used to evaluate the performance of this method relative to constant, annually varying, or random-effect parameter estimates when applied to an occupancy model that simultaneously estimates abundance and detectability in multiple sampling strata. We also demonstrate this method by approximating time-varying abundance using 25 years of detection/non-detection data for 42 Chondrichthyes species off northern Australia. Simulation modelling indicates that the stepwise-Spline Approximation results in lower estimation errors for the proportion of abundance in each stratum, regardless of sample sizes, the underlying form for time-varying abundance and the inclusion of unmodelled process errors. Applied to the Chondrichthyes data from northern Australia, the Spline Approximation identifies temporal variability in abundance for 34 of 42 species, and an annually varying model is never selected. We recommend this stepwise-Spline Approximation in cases where a decision is necessary between constant or annually varying forms for an estimated parameter. Possible applications include occupancy, capture–mark–recapture, catch-at-age and index standardization models.
Yuriy Zakharov - One of the best experts on this subject based on the ideXlab platform.
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polynomial Spline Approximation of clarke s model
IEEE Transactions on Signal Processing, 2004Co-Authors: Yuriy Zakharov, T C Tozer, J F AdlardAbstract:We investigate polynomial Spline Approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation Splines is presented as a series of spectral moments. The optimal Splines outperform the interpolation Splines; however, as the sampling factor increases, the optimal and interpolation Splines of even order tend to provide the same accuracy. To build such Splines, the process to be approximated needs to be known for all time, which is impractical. Local Splines, on the other hand, may be used where the process is known only over a finite interval. We first consider local Splines with quasioptimal Spline coefficients. Then, we derive optimal Spline coefficients and investigate the error for different sets of samples used for calculating the Spline coefficients. In practice, Approximation with a low processing delay is of interest; we investigate local Spline extrapolation with a zero-processing delay. The results of our investigation show that local Spline Approximation is attractive for implementation from viewpoints of both low processing delay and small Approximation error; the error can be very close to the minimum error provided by optimal Splines. Thus, local Splines can be effectively used for channel estimation in multipath fast fading channels.
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Local Spline Approximation of time-varying channel model
Electronics Letters, 2001Co-Authors: Yuriy Zakharov, T C TozerAbstract:Methods of local Spline Approximation of random functions described by Clarke's model are investigated. Such a model is known to describe time-varying amplitudes of multipath components in mobile fading channels. Splines of zero, first and second orders with different Spline coefficients are compared. The comparison shows that local linear and parabolic Splines with quasi-optimal Spline coefficients provide a low Approximation error. This makes them attractive for estimating and modelling fast fading channels.