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An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-11-24 , DOI: 10.1155/2020/9647416
Somayeh Pourghanbar 1 , Jalil Manafian 2 , Mojtaba Ranjbar 1 , Aynura Aliyeva 3 , Yusif S. Gasimov 4, 5, 6
Affiliation  

In this paper, the Saul’yev finite difference scheme for a fully nonlinear partial differential equation with initial and boundary conditions is analyzed. The main advantage of this scheme is that it is unconditionally stable and explicit. Consistency and monotonicity of the scheme are discussed. Several finite difference schemes are used to compare the Saul’yev scheme with them. Numerical illustrations are given to demonstrate the efficiency and robustness of the scheme. In each case, it is found that the elapsed time for the Saul’yev scheme is shortest, and the solution by the Saul’yev scheme is nearest to the Crank–Nicolson method.

中文翻译:

求解非线性偏微分方程的一种有效的交替方向显式方法

本文分析了具有初始和边界条件的完全非线性偏微分方程的Saul'yev有限差分格式。该方案的主要优点是它是无条件稳定和显式的。讨论了该方案的一致性和单调性。使用几种有限差分方案将Saul'yev方案与它们进行比较。数值图示说明了该方案的效率和鲁棒性。在每种情况下,都发现Saul'yev方案的耗时最短,而Saul'yev方案的解最接近Crank-Nicolson方法。
更新日期:2020-11-25
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