<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.</p></abstract>

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear...

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Published Online: Oct 03, 2018

Page range: 255 - 264

Received: Mar 23, 2018

Accepted: Jun 08, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00019

Keywords
Split step method, Semi-linear Parabolic equation, Galerkin-Chebyshev spectral method, Galerkin-Chebyshev pseudo spectral method, Poisson-Boltzman model

© 2018 F. Talay Akyildiz and K. Vajravelu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Published Online: Oct 03, 2018

Page range: 255 - 264

Received: Mar 23, 2018

Accepted: Jun 08, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00019

KeywordsSplit step method, Semi-linear Parabolic equation, Galerkin-Chebyshev spectral method, Galerkin-Chebyshev pseudo spectral method, Poisson-Boltzman model

© 2018 F. Talay Akyildiz and K. Vajravelu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Keywords
Split step method, Semi-linear Parabolic equation, Galerkin-Chebyshev spectral method, Galerkin-Chebyshev pseudo spectral method, Poisson-Boltzman model