A reliable algorithm to compute the approximate solution of KdV-type partial differential equations of order seven

Abstract

The approximate solution of KdV-type partial differential equations of order seven is presented. The algorithm based on one-dimensional Haar wavelet collocation method is adapted for this purpose. One-dimensional Haar wavelet collocation method is verified on Lax equation, Sawada-Kotera-Ito equation and Kaup-Kuperschmidt equation of order seven. The approximated results are displayed by means of tables (consisting point wise errors and maximum absolute errors) to measure the accuracy and proficiency of the scheme in a few number of grid points. Moreover, the approximate solutions and exact solutions are compared graphically, that represent a close match between the two solutions and confirm the adequate behavior of the proposed method.

Solitary Wave Solutions of the Generalized (3+1)-Dimensional Shallow Water-Like Equation by using modified Kudryashov method

“…Nonlinear partial differential equations (NLPDEs) have many application areas such as fluid dynamics, hydromagnetic, optics, physics, chemistry, biology and others [1][2][3][4][5]. With the solutions of these NLPDEs and the values given to the special parameters in these solutions, many physical phenomena we encounter in daily life are modelled [6][7][8][9][10]. Therefore, there has been an increasing interest in the solution methods of NLPDEs by many scientists.…”