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Finite difference schemes for the two‐dimensional semilinear wave equation
Author(s) -
Achouri Talha
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22297
Subject(s) - mathematics , wave equation , norm (philosophy) , convergence (economics) , finite difference , finite difference method , finite difference coefficient , stability (learning theory) , mathematical analysis , finite difference scheme , finite element method , mixed finite element method , computer science , law , physics , machine learning , political science , economics , thermodynamics , economic growth
In this article, two finite difference schemes for solving the semilinear wave equation are proposed. The unique solvability and the stability are discussed. The second‐order accuracy convergence in both time and space in the discrete H 1 ‐norm for the two proposed difference schemes is proved. Numerical experiments are performed to support our theoretical results.