Algorithm to solve nonlinear Advection Equation numerically using cubic Bspline
published by Aِl-Baath University
in 2017
in
and research's language is
العربية
Download
Abstract in English
In this paper, we introduce an algorithm to solve the
Advection equation by finite element method. In this method, we
have chosen Three pattern of cubic B-Spline to approximate the
nonlinear solution to convert the nonlinear PDE into a system of
ODE, Then we solved this system equation by SSP-RK54 method,
And we made a program implementing this algorithm and we
checked the program using some examples, which have exact
solutions, then we evaluate our results. As a conclusion we found
that this method gives accurate results for advection equation.
References used
ARORA G, SINGH BK,-2013-Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method. Appl Math Comput ,224,166–77
BAKODAH HO, 2016-A Comparative Study of Two Spatial Discretization Schemes for Advection equation. International Journal of Modern Nonlinear Theory and Application, 5, 59-66
BELLMAN R, KASHEF BG, CASTI J,1972- Differential quadrature: a technique for the rapid solution of nonlinear differential equations. J Comput Phy, 10,40–52