Numerical investigation of nonlinear generalized regularized long wave equation via delta-shaped basis functions

An International Journal of Optimization and Control: Theories & Applications

article

Ömer Oruç¹ 

[1] Eğil Vocational and Technical Anatolian High School

关键词: Delta-Shaped basis functions;    Nonlinear PDE;    GRLW equation;    Meshless method;    Numerical solution;   

DOI  :  10.11121/ijocta.01.2020.00881

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

In this study we will investigate generalized regularized long wave (GRLW)equation numerically. The GRLW equation is a highly nonlinear partialdifferential equation. We use finite difference approach for timederivatives and linearize the nonlinear equation. Then for space discretizationwe use delta-shaped basis functions which are relatively few studiedbasis functions. By doing so we obtain a linear system of equationswhose solution is used for constructing numerical solution of theGRLW equation. To see efficiency of the proposed method four classictest problems namely the motion of a single solitary wave, interactionof two solitary waves, interaction of three solitary waves and Maxwellianinitial condition are solved. Further, invariants are calculated.The results of numerical simulations are compared with exact solutionsif available and with finite difference, finite element and some collocationmethods. The comparison indicates that the proposed method is favorableand gives accurate results.

【 授权许可】

CC BY