In this work we generate the numerical solutions of the Burgers' equation by applying the Crank-Nicolson method directly to the Burgers' equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers' equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, numerical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution.
In this paper we apply the Du Fort-Frankel finite difference scheme on Burgers equation and solve three test problems. We calculate the numerical solutions using Mathematica 7.0 for different values of viscosity. We have considered smallest value of viscosity as 10 −4 and observe that the numerical solutions are in good agreement with the exact solution.Mathematics Subject Classification 65N06 (Du Fort-Frankel) Mathematica 7.0
In present paper an attempt is made to study the one dimensional formulation of flow in a tube of varying crosssectional area for two phase flow when equilibrium is established eventually and particle volume fraction is taken as one of the additional variable. Conservation laws and shock condition are obtained and using Whitham rule (1974) of characteristic a relation between cross-sectional area and particle volume fraction is obtained and result is discussed for different values of Mach number.
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