The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Farzad Khani - One of the best experts on this subject based on the ideXlab platform.
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the homotopy analysis method to solve the burgers Huxley Equation
Nonlinear Analysis-real World Applications, 2009Co-Authors: A. Molabahrami, Farzad KhaniAbstract:Abstract In this paper, an analytical technique, namely the homotopy analysis method (HAM) is applied to obtain an approximate analytical solution of the Burgers–Huxley Equation. This paper introduces the two theorems which provide us with a simple and convenient way to apply the HAM to the nonlinear PDEs with the power-law nonlinearity. The homotopy analysis method contains the auxiliary parameter ħ , which provides us with a simple way to adjust and control the convergence region of solution series.
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the homotopy analysis method to solve the burgers Huxley Equation
Nonlinear Analysis-real World Applications, 2009Co-Authors: A. Molabahrami, Farzad KhaniAbstract:Abstract In this paper, an analytical technique, namely the homotopy analysis method (HAM) is applied to obtain an approximate analytical solution of the Burgers–Huxley Equation. This paper introduces the two theorems which provide us with a simple and convenient way to apply the HAM to the nonlinear PDEs with the power-law nonlinearity. The homotopy analysis method contains the auxiliary parameter ħ , which provides us with a simple way to adjust and control the convergence region of solution series.
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spectral collocation method and darvishi s preconditionings to solve the generalized burgers Huxley Equation
Communications in Nonlinear Science and Numerical Simulation, 2008Co-Authors: M T Darvishi, S Kheybari, Farzad KhaniAbstract:Abstract In this paper, a numerical solution of the generalized Burgers–Huxley Equation is presented. This is the application of spectral collocation method. To reduce roundoff error in this method we use Darvishi’s preconditionings. The numerical results obtained by this method have been compared with the exact solution. It can be seen that they are in a good agreement with each other, because errors are very small and figures of exact and numerical solutions are very similar.
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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numerical approximation of inhomogeneous time fractional burgers Huxley Equation with b spline functions and caputo derivative
Engineering With Computers, 2021Co-Authors: Abdul Majeed, Mohsin Kamran, Noreen Asghar, Dumitru BaleanuAbstract:A prototype model used to explain the relationship between mechanisms of reaction, convection effects, and transportation of diffusion is the generalized Burgers–Huxley Equation. This study presents numerical solution of non-linear inhomogeneous time fractional Burgers–Huxley Equation using cubic B-spline collocation method. For this purpose, Caputo derivative is used for the temporal derivative which is discretized by L1 formula and spatial derivative is interpolated with the help of B-spline basis functions, so the dependent variable is continuous throughout the solution range. The validity of the proposed scheme is examined by solving four test problems with different initial-boundary conditions. The algorithm for the execution of scheme is also presented. The effect of non-integer parameter $$\alpha $$ and time on dependent variable is studied. Moreover, convergence and stability of the proposed scheme is analyzed, and proved that scheme is unconditionally stable. The accuracy is checked by error norms. Based on obtained results we can say that the proposed scheme is a good addition to the existing schemes for such real-life problems.
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lie symmetry analysis explicit solutions and conservation laws of a spatially two dimensional burgers Huxley Equation
Symmetry, 2020Co-Authors: Amjad Hussain, Dumitru Baleanu, Shahida Bano, Ilyas Khan, Kottakkaran Sooppy NisarAbstract:In this paper, we investigate a spatially two-dimensional Burgers–Huxley Equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems.
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lie symmetry analysis and explicit solutions for the time fractional generalized burgers Huxley Equation
Optical and Quantum Electronics, 2018Co-Authors: Abdullahi Yusuf, Aliyu Isa Aliyu, Dumitru BaleanuAbstract:In this work, we study the time fractional generalized Burgers–Huxley Equation with Riemann–Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing Equation to nonlinear ordinary differential Equation of fractional order using its Lie point symmetries. In the reduced Equation, the derivative is in Erdelyi–Kober sense. We apply power series technique to derive explicit solutions for the reduced Equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
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singularly perturbed burgers Huxley Equation by a meshless method
Thermal Science, 2017Co-Authors: Mir Sajjad Hashemi, Dumitru Baleanu, Hakimeh BarghiAbstract:A meshless method based upon radial basis function (RBF) is utilized to approximate the singularly perturbed Burgers-Huxley (SPBH) Equation with the viscosity coefficient e. The proposed method shows that the obtained solutions are reliable and accurate. Convergence analysis of method was analyzed in a numerical way for different small values of singularity parameter.
Ishak Hashim - One of the best experts on this subject based on the ideXlab platform.
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analytical treatment of generalized burgers Huxley Equation by homotopy analysis method
Bulletin of the Malaysian Mathematical Sciences Society, 2009Co-Authors: Sami A Bataineh, Mohd Salmi Md Noorani, Ishak HashimAbstract:In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley Equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions.
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application of variational iteration method to the generalized burgers Huxley Equation
Chaos Solitons & Fractals, 2008Co-Authors: B Batiha, Mohd Salmi Md Noorani, Ishak HashimAbstract:Abstract In this paper, He’s variational iteration method (VIM) is applied to the generalized Burgers–Huxley Equation. The VIM produces an approximate solution of the Equation without any discretization. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the Equation. Comparisons with the Adomian decomposition method (ADM) reveal that the VIM is very effective and convenient.
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Numerical simulation of the generalized Huxley Equation by He’s variational iteration method
Applied Mathematics and Computation, 2007Co-Authors: B Batiha, Mohd Salmi Md Noorani, Ishak HashimAbstract:Abstract By means of variational iteration method the solution of generalized Huxley Equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials.
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a note on the adomian decomposition method for the generalized Huxley Equation
Applied Mathematics and Computation, 2006Co-Authors: Ishak Hashim, Mohd Salmi Md Noorani, B BatihaAbstract:In a recent paper, Ismail et al. [Adomian decomposition method for Burgers-Huxley and Burgers-Fisher Equations, Appl. Math. Comput. 159 (2004) 291-301] employed the Adomian decomposition method (ADM) to solve, in particular, a generalized nonlinear Huxley Equation. The purpose of this note is to correct Ismail et al.'s numerical solutions of the generalized Huxley Equation. In addition, a convergence proof of the ADM applied to the generalized Huxley Equation is also given.
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solving the generalized burgers Huxley Equation using the adomian decomposition method
Mathematical and Computer Modelling, 2006Co-Authors: Ishak Hashim, Mohd Salmi Md Noorani, M Said R AlhadidiAbstract:In this paper, a convergence proof of the Adomian decomposition method (ADM) applied to the generalized nonlinear Burgers-Huxley Equation is presented. The decomposition scheme obtained from the ADM yields an analytical solution in the form of a rapidly convergent series. The direct symbolic-numeric scheme is shown to be efficient and accurate.
Mohit Nigam - One of the best experts on this subject based on the ideXlab platform.
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a numerical study of singularly perturbed generalized burgers Huxley Equation using three step taylor galerkin method
Computers & Mathematics With Applications, 2011Co-Authors: B Rathish V Kumar, Vivek Sangwan, S V S S N V G K Murthy, Mohit NigamAbstract:In the present work, a numerical study has been carried out for the singularly perturbed generalized Burgers-Huxley Equation using a three-step Taylor-Galerkin finite element method. A Burgers-Huxley Equation represents the traveling wave phenomena. In singular perturbed problems, a very small positive parameter, @e, called the singular perturbation parameter is multiplied with the highest order derivative term. As this parameter tends towards zero, the problem exhibits boundary layers. The traditional methods fail to capture the boundary layers when @e becomes very small. In this paper a three-step Taylor-Galerkin finite element method is used to capture the boundary layers. The method is third-order accurate and has inbuilt upwinding. Stability analysis has been carried out and the numerical results show that the method is efficient in capturing the boundary layers.
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three step taylor galerkin method for singularly perturbed generalized hodgkin Huxley Equation
International Journal of Modeling Simulation and Scientific Computing, 2010Co-Authors: Vivek Sangwan, B Rathish V Kumar, S V S S N V G K Murthy, Mohit NigamAbstract:A numerical study is carried out for the singularly perturbed generalized Hodgkin–Huxley Equation. The Equation is nonlinear which mimics the ionic processes at a real nerve membrane. A small parameter called singular perturbation parameter is introduced in the highest order derivative term. Keeping other parameters fixed, as this singular perturbation parameter approaches to zero, a boundary layer occurs in the solution. Three-step Taylor Galerkin finite element method is employed on a piecewise uniform Shishkin mesh to solve the Equation. To procure more accurate temporal differencing, the method employs forward-time Taylor series expansion including time derivatives of third order which are evaluated from the governing singularly perturbed generalized Hodgkin–Huxley Equation. This yields a generalized time-discretized Equation which is successively discretized in space by means of the standard Bubnov–Galerkin finite element method. The method is third-order accurate in time. The code based on the purposed scheme has been validated against the cases for which the exact solution is available. It is also observed that for the Singularly Perturbed Generalized Hodgkin–Huxley Equation, the boundary layer in the solution manifests not only by varying the singular perturbation parameter but also by varying the other parameters appearing in the model.
Manil T Mohan - One of the best experts on this subject based on the ideXlab platform.
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conforming nonconforming and dg methods for the stationary generalized burgers Huxley Equation
Journal of Scientific Computing, 2021Co-Authors: Arbaz Khan, Manil T Mohan, Ricardo RuizbaierAbstract:In this work we address the analysis of the stationary generalized Burgers-Huxley Equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for its numerical approximation. The existence, uniqueness and regularity of weak solutions are discussed in detail using a Faedo-Galerkin approach and fixed-point theory, and a priori error estimates for all three types of numerical schemes are rigorously derived. A set of computational results are presented to show the efficacy of the proposed methods.
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large deviation principle for occupation measures of stochastic generalized burgers Huxley Equation
arXiv: Probability, 2021Co-Authors: Ankit Kumar, Manil T MohanAbstract:The present work deals with the global solvability as well as asymptotic analysis of stochastic generalized Burgers-Huxley (SGBH) Equation perturbed by space-time white noise in a bounded interval of $\mathbb{R}$. We first prove the existence of unique mild as well as strong solution to SGBH Equation and then obtain the existence of an invariant measure. Later, we establish two major properties of the Markovian semigroup associated with the solutions of SGBH Equation, that is, irreducibility and strong Feller property. These two properties guarantees the uniqueness of invariant measures and ergodicity also. Then, under further assumptions on the noise coefficient, we discuss the ergodic behavior of the solution of SGBH Equation by providing a Large Deviation Principle (LDP) for the occupation measure for large time (Donsker-Varadhan), which describes the exact rate of exponential convergence.
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mild solutions for the stochastic generalized burgers Huxley Equation
Journal of Theoretical Probability, 2021Co-Authors: Manil T MohanAbstract:In this work, we consider the stochastic generalized Burgers–Huxley Equation perturbed by space–time white noise and discuss the global solvability results. We show the existence of a unique global mild solution to such Equation using a fixed point method and stopping time arguments. The existence of a local mild solution (up to a stopping time) is proved via contraction mapping principle. Then, establishing a uniform bound for the solution, we show the existence and uniqueness of global mild solution to the stochastic generalized Burgers–Huxley Equation. Finally, we discuss the inviscid limit of the stochastic Burgers–Huxley Equation to the stochastic Burgers as well as Huxley Equations.
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on the generalized burgers Huxley Equation existence uniqueness regularity global attractors and numerical studies
Discrete and Continuous Dynamical Systems-series B, 2021Co-Authors: Manil T Mohan, Arbaz KhanAbstract:In this work, we consider the forced generalized Burgers-Huxley Equation and establish the existence and uniqueness of a global weak solution using a Faedo-Galerkin approximation method. Under smoothness assumptions on the initial data and external forcing, we also obtain further regularity results of weak solutions. Taking external forcing to be zero, a positivity result as well as a bound on the classical solution are also established. Furthermore, we examine the long-term behavior of solutions of the generalized Burgers-Huxley Equations. We first establish the existence of absorbing balls in appropriate spaces for the semigroup associated with the solutions and then show the existence of a global attractor for the system. The inviscid limits of the Burgers-Huxley Equations to the Burgers as well as Huxley Equations are also discussed. Next, we consider the stationary Burgers-Huxley Equation and establish the existence and uniqueness of weak solution by using a Faedo-Galerkin approximation technique and compactness arguments. Then, we discuss about the exponential stability of stationary solutions. Concerning numerical studies, we first derive error estimates for the semidiscrete Galerkin approximation. Finally, we present two computational examples to show the convergence numerically.
