Numerical Solutions of Time Dependent Partial Differential Equations Using Weighted Residual Method With Piecewise Polynomials

Authors

  • Muntasir Alam Department of Applied Mathematics, Dhaka University, Dhaka-1000, Bangladesh
  • Md Shafiqul Islam Department of Applied Mathematics, Dhaka University, Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.3329/dujs.v67i1.54566

Keywords:

Diffusion equation, wave equation, Galerkin Weighted Residual method, Bernstein, Legendre and Bernoulli Polynomials.

Abstract

We use Galerkin weighted residual (GWR) method to solve one dimensional heat and wave equations as initial and boundary value problems (IBVPs) numerically. Three special types of piecewise polynomials namely: Bernstein, Bernoulli and Legendre polynomials are used as basis functions to solve these IBVPs. A few examples are tested by the proposed method and then the results are compared with the solutions found in other existing methods. The numerical results obtained in this paper are in good agreement with the exact solutions.

Dhaka Univ. J. Sci. 67(1): 5-12, 2019 (January)

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Published

2019-01-30

How to Cite

Alam, M., & Islam, M. S. (2019). Numerical Solutions of Time Dependent Partial Differential Equations Using Weighted Residual Method With Piecewise Polynomials. Dhaka University Journal of Science, 67(1), 5–12. https://doi.org/10.3329/dujs.v67i1.54566

Issue

Vol. 67 No. 1 (2019)

Section

Articles