Статья

A multi-resolution hybrid Haar wavelet collocation method for solving nonlinear partial differential equations

Amina IqbalDepartment of Mathematics, Lahore College for Women University, Lahore, PakistanShazia JavedDepartment of Mathematics, Lahore College for Women University, Lahore, PakistanSidra SaleemDepartment of Mathematics, Lahore College for Women University, Lahore, PakistanMohammad NasirDepartment of Physics, Faculty of Sciences University of Sialkot 51040 Sialkot, PakistanNazir Ahmad ChoudhryDepartment of Mathematics, Faculty of Sciences University of Sialkot 51040 Sialkot, PakistanDalia H. ElkamchouchiDepartment of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaUmid TurdialiyevDoctor of Technical Sciences, Department of Organic Chemistry, Rector, Andijan State Technical Institute, Bobur Avenue, 56. Andijan, UzbekistanM.Ijaz KhanDepartment of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, Al-Khobar, Saudi Arabia

Ain Shams Engineering Journaljournal2026en

ABI

Аннотация

This study focuses on approximation of several types of partial differential equations with different orders (including diffusion equation, Fisher equation, Atangana-Baleanu Burger’s equation and Korteweg-de Vries (KdV) equation). A multi-resolution (MR) based hybrid Haar wavelet collocation method (hHWCM) is proposed to approximate the exact solutions of discussed equations. The proposed method (hHWCM) is constructed on the basis of Euler’s formula (finite difference method (FDM)) and collocation procedure of Haar wavelet (HW) having multi-resolution characteristics. The algorithm of hHWCM is formulated using MATLAB coding. The nonlinear PDEs are linearized using Quasi Newton’s Technique [1] , whereas time discretization is performed using FDM and space discretization is obtained by HWCM. A comparative analysis between exact and approximate solutions is attained and stability of the proposed method is discussed. Moreover, the maximum absolute errors (MAEs) and experimental rate of convergence (ERoC) are calculated. The evaluations are displayed by means of figures and tables that indicate a good compatibility between the two solutions.

Темы

Fractional Differential Equations Solutions Nonlinear Waves and Solitons Iterative Methods for Nonlinear Equations

Идентификаторы

DOI: 10.1016/j.asej.2026.104117

Цитирования и источники

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