用非标准有限差分法求解具有内层的微分-差分方程

R. Omkar, M. Lalu, K. Phaneendra
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引用次数: 0

摘要

研究一类具有内层性质的微分-差分型方程的解。提出了用非标准有限差分法求解该方程的差分格式。有限差分是由一阶和二阶导数导出的。利用这些近似,将给定方程离散化。采用该算法对三对角线系统的离散方程进行求解。对该方法进行了收敛性检验。数值算例验证了该方法的有效性。最大误差的解决方案,在对比其他方法组织证明该方法。示例解中的层行为用图来描述。
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Numerical solution of differential-difference equations having an interior layer using nonstandard finite differences
This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.
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来源期刊
CiteScore
1.20
自引率
50.00%
发文量
50
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