Numerical Solution of Emden–Fowler Heat-Type Equations Using Backward Difference Scheme and Haar Wavelet Collocation Method

Mohammed N. Alshehri (), Ashish Kumar, Pranay Goswami, Saad Althobaiti and Abdulrahman F. Aljohani
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Mohammed N. Alshehri: Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia
Ashish Kumar: School of Liberal Studies, Dr B.R. Ambedkar University Delhi, Delhi 110006, India
Pranay Goswami: School of Liberal Studies, Dr B.R. Ambedkar University Delhi, Delhi 110006, India
Saad Althobaiti: Department of Sciences and Technology, Ranyah University Collage, Taif University, Taif 21944, Saudi Arabia
Abdulrahman F. Aljohani: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia

Mathematics, 2024, vol. 12, issue 23, 1-15

Abstract: In this study, we introduce an algorithm that utilizes the Haar wavelet collocation method to solve the time-dependent Emden–Fowler equation. This proposed method effectively addresses both linear and nonlinear partial differential equations. It is a numerical technique where the differential equation is discretized using Haar basis functions. A difference scheme is also applied to approximate the time derivative. By leveraging Haar functions and the difference scheme, we form a system of equations, which is then solved for Haar coefficients using MATLAB software. The effectiveness of this technique is demonstrated through various examples. Numerical simulations are performed, and the results are presented in graphical and tabular formats. We also provide a convergence analysis and an error analysis for this method. Furthermore, approximate solutions are compared with those obtained from other methods to highlight the accuracy, efficiency, and computational convenience of this technique.

Keywords: Emden–Fowler type equations; numerical method; backward difference scheme; Haar wavelet method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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