Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term

被引：5

作者：

Zadvan, Homa ^{[1
]}

Rashidinia, Jalil ^{[1
]}

机构：

[1] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran 13185768, Iran

来源：

NUMERICAL ALGORITHMS | 2017年 / 74卷 / 02期

关键词：

Non-polynomial spline approximation; Two-dimensional wave equation; Stability analysis; Sine-Gordon equation; 2 SPACE DIMENSIONS; HYPERBOLIC TELEGRAPH EQUATION; STABLE DIFFERENCE SCHEME; TIME INTEGRATION SCHEME; SINE-GORDON EQUATION; NUMERICAL-SOLUTION; VARIABLE-COEFFICIENTS; COLLOCATION METHOD;

D O I：

10.1007/s11075-016-0149-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, two classes of methods are developed for the solution of two space dimensional wave equations with a nonlinear source term. We have used non-polynomial cubic spline function approximations in both space directions. The methods involve some parameters, by suitable choices of the parameters, a new high accuracy three time level scheme of order O(h (4) + k (4) + tau (2) + tau (2) h (2) + tau (2) k (2)) has been obtained. Stability analysis of the methods have been carried out. The results of some test problems are included to demonstrate the practical usefulness of the proposed methods. The numerical results for the solution of two dimensional sine-Gordon equation are compared with those already available in literature.

引用

页码：289 / 306

页数：18

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