Meshless method of approximate particular solution for an initial and boundary value problem of the Korteweg–de Vries type equation and eventual periodicity

Partial Differential Equations in Applied Mathematics

卷:4

Sajjad Hussain Shah¹  Anup Lamichhane²  Muhammad Usman³  Marjan Uddin⁴ 

[1] Corresponding author.;

[2] Technology Peshawar, Pakistan;

[3] University of Dayton, 300 College Park, Dayton OH 45469-2316, USA;

[4] University of Engineering &

关键词: KdV equation;    Eventual periodicity;    Radial basis functions;    Meshless method of approximate particular solution;    Method of approximate particular solution;    MAPS;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this work, we approximate the solution of an IBVP of the Korteweg–de Vries type equation with periodic forcing at the boundary using the meshless method of approximate particular solution (MMAPS). This method is based on radial basis functions (RBFs). Further, it is shown that the solution exhibits the eventual periodicity and method approximates the solution accurately and efficiently. To test the accuracy of the method the conserved quantities are also computed for the KdV equation. The accuracy of the method depends on the shape parameter and the optimal value of the shape parameter is also approximated.

【 授权许可】

Unknown