BERNOULLI WAVELET COLLOCATION APPROACH FOR FRACTIONAL ZAKHAROV-KUZNETSOV EQUATION
By
S. Kumbinarasaiah1, R. Yeshwanth2 and S. Dhawan3
1,2Department of Mathematics, Bangalore University, Bengaluru, Karnataka, India-560056
3Department of Mathematics, CCS HAU Haryana, India-125004.
Email: kumbinarasaiah@bub.ernet.in, yeshwanth@bub.ernet.in, sharanjeet@hau.ac.in
(Received: October 09, 2023; In format: May 21, 2025; Revised: June 2024, 2015; Accepted: July 04, 2025)
DOI: https://doi.org/10.58250/jnanabha_SI.2025.55106
Abstract
Fractional partial differential equations (PDEs) of particular classes, like the nonlinear fractional Zakharov-Kuznetsov equation, are the subject of this work. We propose a novel methodology, the Bernoulli wavelet collocation method (BWCM ). A collocation approach based on the Bernoulli wavelets is used to solve such equations. After that, we translate the mathematical model into an algebraic system of equations by utilizing the wavelet features. One can obtain an approximation answer using the Newton-Raphson method to solve these algebraic equations. Tables and graphs are used to analyze and compare the results with other methods reported in the literature. With the help of suitable parameter settings and a thorough explanation of the physical behavior of the solutions, these results are visually described. Two numerical problems are provided to demonstrate the precision of the stated approach. Many fractional PDEs, as is well known, lack exact solutions, and several semi-analytical approaches depend on regulating parameters to function; however, this method is parameter-free. It also takes less time to run the applications and is simple to apply. The numerical method based on wavelets that
have been proposed is efficient and appealing from a computational standpoint. The suggested method’s convergence analysis is presented in terms of the theorem. The numerical computations and visualizations are done in Matlab.
2020 Mathematical Sciences Classification: 65M70, 65T60
Keywords and Phrases: Partial differential equations; Collocation method; Integration; Bernoulli wavelets; Newton Raphson technique