TITLE:
Numerical Solution of the Coupled Viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis
AUTHORS:
Masho Jima, Alemayehu Shiferaw, Ali Tsegaye
KEYWORDS:
Differential Quadrature Method, Fourier Expansion, Coupled Viscous, Coupled Viscous Burgers’ Equation, Initial and Boundary Conditions
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.7,
July
30,
2018
ABSTRACT:
The differential quadrature method based on Fourier expansion basis is applied
in this work to solve coupled viscous Burgers’ equation with appropriate
initial and boundary conditions. In the first step for the given problem we
have discretized the interval and replaced the differential equation by the Differential
quadrature method based on Fourier expansion basis to obtain a system
of ordinary differential equation (ODE) then we implement the numerical
scheme by computer programing and perform numerical solution. Finally
the validation of the present scheme is demonstrated by numerical example
and compared with some existing numerical methods in literature. The method
is analyzed for stability and convergence. It is found that the proposed
numerical scheme produces a good result as compared to other researcher’s
result and even generates a value at the nodes or mesh points that the results
have not seen yet.