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A simple algorithm for numerical solution of nonlinear parabolic partial differential equations

  • Sidra Saleem
  • Imran AzizEmail author
  • Malik Zawwar Hussain
Original Article

Abstract

In this paper, numerical solution of nonlinear two-dimensional parabolic partial differential equations with initial and Dirichlet boundary conditions is considered. The time derivative is approximated using finite difference scheme whereas space derivatives are approximated using Haar wavelet collocation method. The proposed method is developed for semilinear and quasilinear cases, however, it can easily be extended to other types of nonlinearities as well. The proposed method is also illustrated for nonlinear heat equation and Burgers’ equation. The proposed method is implemented upon five test problems and the numerical results are shown using tables and figures. The numerical results validate the accuracy and efficiency of the proposed method.

Keywords

Haar wavelet Parabolic PDE Nonlinear heat equation Burgers’ equation 

Notes

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsUniversity of PeshawarPeshawarPakistan

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