STABLE ALGORITHM FOR THE WAVE EQUATION USING FINITE DIFFERENCE METHOD

The numerical solution of hyperbolic equations has shown instabilities in some studies (see [2]). In this paper, we use a trick to remedy the reasons for instabilities of particular example of hyperbolic equation, namely the wave equation. We propose a simple method based on the finite difference me...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 3; p. 998
Main Author Loumi, A
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Algorithms
Analysis
Boundary conditions
Differential equations
Energy
Energy conservation
Finite difference method
Mathematical analysis
Methods
Partial differential equations
Wave equations
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Summary:The numerical solution of hyperbolic equations has shown instabilities in some studies (see [2]). In this paper, we use a trick to remedy the reasons for instabilities of particular example of hyperbolic equation, namely the wave equation. We propose a simple method based on the finite difference method and the projection on a manifold that conserves energy. Keywords: wave equation, projection, finite difference method. AMS Subject Classification: 33F05, 58J45, 65M22.
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ISSN:2146-1147
2146-1147