Short Communication Approximation of Harry Dym Equation via Local RBF Method

Harry Dym Equation via RBF Method

  • Hameed Ullah Jan Department of Mathematics, University of Science and Technology Bannu, Khyber Pakhtunkhwa-28100, Pakistan
  • Tahir Khan Department of Mathematics, University of Science and Technology Bannu, Khyber Pakhtunkhwa-28100, Pakistan
  • Irshad Ali Shah Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology, Peshawar-25120, Pakistan
  • Muhammad Zubair Khan Department of Mathematics, University of Science and Technology Bannu, Khyber Pakhtunkhwa-28100, Pakistan
Keywords: partial differential equations (PDEs), harry dym (HD) equation, meshfree approache, RBF methods, local-RBF method

Abstract

 

Differential equations, which can be found in many branches of physics and engineering which are produced through mathematical modeling of many physical systems. A crucial dynamical equation that has uses in a number of physical systems is the HD equation. This is one of the significant nonlinear evolution equation that comes up when studying solitons. In this paper, the HD equation is numerically solved using a local radial basis function (LRBF) approach with the goal of creating local spatial approximation at each point in space as a consequence of local methodology. To deal with time variable, Runge-Kutta scheme of order four is applied. For proving suggested method accuracy and efficiency some error norms viz LRMS, Loo and L2 of test problems are calculated. The solutions obtained by LRBF method are also compared to past studies, and the results of proposed approach are better and more closely match to the exact solution.

 

Published
2025-03-11
Issue
Vol 68 No 1 (2025): Pakistan Journal of Scientific and Industrial Research Series A: Physical Sciences
Section
Articles