<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in <italic>L</italic><sup>2</sup>-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.</p></abstract>

The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in L2-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.

Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

Department of Mathematics and Informatics

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization,...

Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

Published Online: Oct 10, 2020

Page range: 303 - 317

Received: May 25, 2020

Accepted: Oct 01, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0023

Keywords
Numerical solution, Pseudo-spectral method, Parabolic equation, Non-local boundary conditions, Error estimate

© 2020 Abdeldjalil Chattouh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

Published Online: Oct 10, 2020

Page range: 303 - 317

Received: May 25, 2020

Accepted: Oct 01, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0023

KeywordsNumerical solution, Pseudo-spectral method, Parabolic equation, Non-local boundary conditions, Error estimate

© 2020 Abdeldjalil Chattouh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Numerical solution, Pseudo-spectral method, Parabolic equation, Non-local boundary conditions, Error estimate