On the Computational Efficiency of Two-Dimensional Haar Wavelet Schemes for Solving Nonlinear Evolutionary PDEs

Document Type : Research Paper

Authors
Ankita Yadav 1
Narendra Kumar 2
Amit K. Verma 1
Ravi P. Agarwal 3
1 Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna 801106, (BR) India
2 Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Jodhpur 342030, Rajasthan, India
3 Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
10.22055/jacm.2025.48600.5354
Abstract
This paper presents collocation methods employing two-dimensional uniform and non-uniform Haar wavelet, integrated with the Newton–Raphson iterative algorithm, for the efficient solution of nonlinear partial differential equations (PDEs). The proposed approaches are specifically applied to the generalized Benjamin–Bona–Mahony–Burgers’ equation and the generalized Rosenau–KdV–RLW equation. A rigorous theoretical analysis is provided to establish the convergence behavior of both methods. To assess their accuracy and computational performance, a series of benchmark problems are examined across a range of parameter values. The numerical results reveal remarkable accuracy, even with coarse spatial discretization. Furthermore, a comparative evaluation against existing methods demonstrates the enhanced efficiency and robustness of the proposed techniques.
Keywords
Haar wavelet
Uniform and Non-uniform grids
Benjamin&ndash
Bona&ndash
Mahony&ndash
Burgers&rsquo
equation
Rosenau&ndash
KdV&ndash
RLW equation
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Journal of Applied and Computational Mechanics
Volume 12, Issue 2
Spring 2026
Pages 523-540