Open AccessOne-dimensional coupled Burgers’ equation and its numerical solution by an implicit logarithmic finite-difference method
Author(s) -
Vineet K. Srivastava,
Mohammad Tamsir,
Mukesh Kumar Awasthi,
Sarita Singh
Publication year - 2014
Publication title -
aip advances
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 58
ISSN - 2158-3226
DOI - 10.1063/1.4869637
Subject(s) - logarithm , nonlinear system , burgers' equation , mathematics , numerical analysis , finite difference method , newton's method , finite difference , mathematical analysis , partial differential equation , scheme (mathematics) , exact solutions in general relativity , physics , quantum mechanics
In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available