A New Approach for Numerical Solution of Modified Korteweg-de Vries Equation

被引：23

作者：

Ak, Turgut ^{[1
]}

Karakoc, S. Battal Gazi ^{[2
]}

Biswas, Anjan ^{[3
,4
]}

机构：

[1] Yalova Univ, Fac Engn, Dept Transportat Engn, TR-77100 Yalova, Turkey

[2] Nevsehir Haci Bektas Veli Univ, Fac Sci & Art, Dept Math, TR-50300 Nevsehir, Turkey

[3] Delaware State Univ, Dept Math Sci, Dover, DE 19901 USA

[4] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

来源：

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE | 2017年 / 41卷 / A4期

关键词：

Modified KdV equation; Galerkin method; Solitary waves; Soliton; B-spline; 1-SOLITON SOLUTION; SOLITON-SOLUTIONS; KDV EQUATION; BOUSSINESQ; BURGER; LAW;

D O I：

10.1007/s40995-017-0238-5

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, a lumped Galerkin method is applied with cubic B-spline interpolation functions to find the numerical solution of the modified Korteweg-de Vries (mKdV) equation. Test problems including motion of single solitary wave, interaction of two solitons, interaction of three solitons, and evolution of solitons are solved to verify the proposed method by calculating the error norms L-2 and L-infinity and the conserved quantities mass, momentum and energy. Applying the von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Consequently, the obtained results are found to be harmony with the some recent results.

引用

页码：1109 / 1121

页数：13

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