Open AccessNumerical Solutions of Time Dependent Partial Differential Equations Using Weighted Residual Method With Piecewise Polynomials
Author(s) -
M. Shahria Alam,
Shafiqul Islam
Publication year - 2019
Publication title -
the dhaka university journal of science
Language(s) - English
Resource type - Journals
eISSN - 2408-8528
pISSN - 1022-2502
DOI - 10.3329/dujs.v67i1.54566
Subject(s) - legendre polynomials , piecewise , method of mean weighted residuals , mathematics , residual , galerkin method , boundary value problem , partial differential equation , bernoulli polynomials , mathematical analysis , numerical analysis , classical orthogonal polynomials , orthogonal polynomials , finite element method , algorithm , physics , thermodynamics
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)