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Volume 33, Issue 4
Study of a Generalized Nonlinear Euler-Poisson-Darboux System: Numerical and Bessel Based Solutions

Chteoui Riadh, Arfaoui Sabrine & Ben Mabrouk Anouar

DOI: 10.4208/jpde.v33.n4.2

J. Part. Diff. Eq., 33 (2020), pp. 313-340.

Published online: 2020-08

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  • 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.

  • Keywords

Finite difference method, Lyapunov-Sylvester operators, generalized Euler-Poisson-Darboux equation, hyperbolic equation, Lauricella hypergeometric functions.

  • AMS Subject Headings

65M06, 65M12, 65M22, 35Q05, 35L80, 35C65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

riadh.chteoui.fsm@gmail.com (Chteoui Riadh)

sabrine.arfaoui@issatm.rnu.tn (Arfaoui Sabrine)

anouar.benmabrouk@fsm.rnu.tn (Ben Mabrouk Anouar)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-313, author = {Riadh , ChteouiSabrine , Arfaoui and Anouar , Ben Mabrouk}, title = {Study of a Generalized Nonlinear Euler-Poisson-Darboux System: Numerical and Bessel Based Solutions}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {4}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/17862.html} }
TY - JOUR T1 - Study of a Generalized Nonlinear Euler-Poisson-Darboux System: Numerical and Bessel Based Solutions AU - Riadh , Chteoui AU - Sabrine , Arfaoui AU - Anouar , Ben Mabrouk JO - Journal of Partial Differential Equations VL - 4 SP - 313 EP - 340 PY - 2020 DA - 2020/08 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n4.2 UR - https://global-sci.org/intro/article_detail/jpde/17862.html KW - Finite difference method, Lyapunov-Sylvester operators, generalized Euler-Poisson-Darboux equation, hyperbolic equation, Lauricella hypergeometric functions. AB -

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.

Riadh , ChteouiSabrine , Arfaoui and Anouar , Ben Mabrouk. (2020). Study of a Generalized Nonlinear Euler-Poisson-Darboux System: Numerical and Bessel Based Solutions. Journal of Partial Differential Equations. 33 (4). 313-340. doi:10.4208/jpde.v33.n4.2
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