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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohammed N. Alshehri & Ashish Kumar & Pranay Goswami & Saad Althobaiti & Abdulrahman F. Aljohani, 2024. "Numerical Solution of Emden–Fowler Heat-Type Equations Using Backward Difference Scheme and Haar Wavelet Collocation Method," Mathematics, MDPI, vol. 12(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3692-:d:1529172
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    References listed on IDEAS

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    1. Mehdi Dehghan, 2003. "On the numerical solution of the diffusion equation with a nonlocal boundary condition," Mathematical Problems in Engineering, Hindawi, vol. 2003, pages 1-12, January.
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