A NUMERICAL SCHEME FOR NONLINEAR KLEIN-GORDON EQUATIONS
A NUMERICAL SCHEME FOR NONLINEAR KLEIN-GORDON EQUATIONS
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发表时间：
1983
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通讯作者：
Luis
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作者：
Luis
有限差分法是数学物理中求解非线性波动方程的一种有效方法。其中的关键问题是如何处理非线性项.本文发展了非线性Klein-Gordon方程的数值格式，并利用[2-5]的技巧建立了误差估计.在Stetter[7]和郭本禹[2-6]给出的非线性格式理论的基础上，由误差估计得到了该格式的稳定性，若Klein-Gordon方程的解具有光滑导数，则这种稳定性蕴含收敛性。
The finite difference method is useful in mathematical physics for solving the nonlinear wave equations. The key problem involved is how to deal with the nonlinear term.In this paper, numerical scheme for nonlinear Klein-Gordon equation is developed and an error estimation is established with the technique of [2-5].Based on the theory of nonlinear scheme given by Stetter[7] and Guo Benyu[2-6], the stability of this scheme is obtained from the error estimation.If the solution of Klein-Gordon equation has smooth derivatives andthen such stability implies the convergence.