Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable

Chinese Quarterly Journal of Mathematics ›› 1997, Vol. 12 ›› Issue (3): 35-40.

Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable

Institute of Computational and Applied Mathematics;Xiangtan University,Hunan,411105;Laboratory of ComputationalPhysics,Institute of Applied Phyics and Computational Mathematics,Beijing,100088;Graduate School of ChinaAcademy of Engineering Physics,Beijing,100088；Xinjiang C.P.College of Army Corps,Changji,Xinjiang

Received:1995-08-29 Online:1997-09-30 Published:2024-11-22
Supported by:
The Project Supported by National Natural Science Foundation of China.

Abstract

Abstract: In this paper,the convergence and stability of the 'Leap-frog' finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).

Key words: , semilinear wave equation, Leap-frog finite difference scheme, convergence and stability

CLC Number:

O175

Lu Bainian, Fang Shaomei. Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable[J]. Chinese Quarterly Journal of Mathematics, 1997, 12(3): 35-40.

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Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable

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