Year: 2020
Author: Ben Mabrouk Anouar, Chteoui Riadh, Arfaoui Sabrine, Ben Mabrouk Anouar
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 4 : pp. 313–340
Abstract
In this paper a nonlinear Euler-Poisson-Darboux system is considered. In a first part, we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel type differential equations. Next, a finite difference scheme in two-dimensional case has been developed. The continuous system is transformed into an algebraic quasi linear discrete one leading to generalized Lyapunov-Sylvester operators. The discrete algebraic system is proved to be uniquely solvable, stable and convergent based on Lyapunov criterion of stability and Lax-Richtmyer equivalence theorem for the convergence. A numerical example has been provided at the end to illustrate the efficiency of the numerical scheme developed in section 3. The present method is thus proved to be more accurate than existing ones and lead to faster algorithms.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v33.n4.2
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 4 : pp. 313–340
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Finite difference method Lyapunov-Sylvester operators generalized Euler-Poisson-Darboux equation hyperbolic equation Lauricella hypergeometric functions.