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首页> 外文期刊>Computer physics communications >Tension spline approach for the numerical solution of nonlinear Klein–Gordon equation
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Tension spline approach for the numerical solution of nonlinear Klein–Gordon equation

机译：张力样条法求解非线性Klein-Gordon方程的数值解

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摘要

The nonlinear Klein–Gordon equation describes a variety of physical phenomena such as dislocations, ferroelectric and ferromagnetic domain walls, DNA dynamics, and Josephson junctions. We derive approximate expressions for the dispersion relation of the nonlinear Klein–Gordon equation in the case of strong nonlinearities using a method based on the tension spline function and finite difference approximations. The resulting spline difference schemes are analyzed for local truncation error, stability and convergence. It has been shown that by suitably choosing the parameters, we can obtain two schemes of O(k2 +k2h2 +h2) and O(k2 +k2h2 +h4). In the end, some numerical examples are provided to demonstrate the effectiveness of the proposed schemes.
机译：非线性Klein-Gordon方程描述了各种物理现象，例如位错，铁电和铁磁畴壁，DNA动力学和约瑟夫森结。在强非线性的情况下，我们使用基于张力样条函数和有限差分逼近的方法来推导非线性Klein-Gordon方程的色散关系的近似表达式。分析所得样条差方案的局部截断误差，稳定性和收敛性。已经表明，通过适当地选择参数，我们可以获得O（k2 + k2h2 + h2）和O（k2 + k2h2 + h4）的两种方案。最后，提供了一些数值示例来说明所提出方案的有效性。

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