Abstract
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.
Highlights
Let us consider one dimensional coupled nonlinear Burgers’ equation[1,2] in generalized form: ∂u ∂t + δ ∂ ∂ 2u x2 ηu ∂u ∂x α ∂v u∂x ∂u v∂x = 0
Various researchers have proposed analytical solution to one dimensional coupled Burgers’ equation, e.g. Kaya[4] used Adomian decomposition method, Soliman[5] applied a modified extended tanh-function method, whereas numerical solutions to this system of equation have been attempted by many researchers
The efficiency and reliability of the implicit logarithmic finite-difference method (I-LFDM) scheme is illustrated through three numerical examples
Summary
Let us consider one dimensional coupled nonlinear Burgers’ equation[1,2] in generalized form:.
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