Rothe–Legendre pseudospectral method for a semilinear pseudoparabolic equation with nonclassical boundary condition
Articles
Abdeldjalil Chattouh
Khenchela University
https://orcid.org/0000-0001-5962-0966
Khaled Saoudi
Khenchela University
https://orcid.org/0000-0003-1249-8857
Maroua Nouar
Khenchela University
https://orcid.org/0000-0001-9521-763X
Published 2022-01-01
https://doi.org/10.15388/namc.2022.27.25187
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Keywords

pseudoparabolic equation
nonlocal conditions
Rothe method
solvability
pseudospectral method

How to Cite

Chattouh A., Saoudi K. and Nouar M. (2022) “Rothe–Legendre pseudospectral method for a semilinear pseudoparabolic equation with nonclassical boundary condition”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 38-53. doi: 10.15388/namc.2022.27.25187.

Abstract

A semilinear pseudoparabolic equation with nonlocal integral boundary conditions is studied in the present paper. Using Rothe method, which is based on backward Euler finitedifference schema, we designed a suitable semidiscretization in time to approximate the original problem by a sequence of standard elliptic problems. The questions of convergence of the approximation scheme as well as the existence and uniqueness of the solution are investigated. Moreover, the Legendre pseudospectral method is employed to discretize the time-discrete approximation scheme in the space direction. The main advantage of the proposed approach lies in the fact that the full-discretization schema leads to a symmetric linear algebraic system, which may be useful for theoretical and practical reasons. Finally, numerical experiments are included to illustrate the effectiveness and robustness of the presented algorithm.

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