Energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon equation and coupled sine-Gordon equations

被引:5
|
作者
Deng, Dingwen [1 ]
Chen, Jingliang [1 ]
Wang, Qihong [1 ]
机构
[1] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Peoples R China
基金
中国国家自然科学基金;
关键词
Sine-Gordon equations; Coupled sine-Gordon equations; Du Fort-Frankel difference schemes; Energy conservations; Error estimations; NUMERICAL-SOLUTION; CONVERGENCE; ALGORITHMS; STABILITY; 2ND-ORDER; MODEL;
D O I
10.1007/s11075-022-01453-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Du Fort-Frankel (DFF) finite difference method (FDM) was proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953. It is an explicit and unconditionally von Neumann stable scheme. Thus, it is very easy to be implemented and suitable for long-term simulations. However, there has been no research work on numerical solutions of sine-Gordon equations (SGE) and nonlinear coupled sine-Gordon equations (CSGEs) by using energy-preserving Du Fort-Frankel finite difference methods (EP-DFF-FDMs). In this study, two classes of weighted EP-DFF-FDMs, which are devised by combining DFF FDMs with invariant energy quadratization methods (IEQMs), are suggested for numerical simulations of SGE and CSGEs, respectively. By using the discrete energy method, it is shown that their solutions satisfy the discrete energy conservative laws, and converge to exact solutions with an order of O(tau(2) + h(x)(2) + h(y)(2) +( tau|h(x) )(2) + ( tau|h(y) )(2)) in H-1-norm.Here, tau denotes time increment, while hx and hy represent spacing grids in x- and y-dimensions, respectively. What is more, our methods with parameter theta >= 1/4 are unconditionally stable in L-2-norm though they are explicit schemes. Finally, numerical results confirm the exactness of theoretical findings, and the superiorities of our algorithms over some existent algorithms in terms of computational efficiency and the ability to conserve the discrete energy.
引用
收藏
页码:1045 / 1081
页数:37
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