Finite Differences Methods for solving Korteweg-de Vries-Burger's Equation
AL-Rafidain Journal of Computer Sciences and Mathematics,
2011, Volume 8, Issue 1, Pages 65-80
AbstractIn this paper we solved the Korteweg-de Vries-Burger's equation numerically by finite difference methods, using two different schemes which are the Fully Implicit scheme and the Exponential finite difference scheme, because of the existence of the third derivative in the equation we suggested a treatment for the numerical solution by parting the mesh grid into five regions, the first region represents the first boundary condition, the second one at the grid point , while the third represents the grid points , the fourth represents the grid point and the fifth is for the second boundary condition .
We also studied the numerical stability, using Fourier (Von-Neumann) method for the two schemes which used in the solution on all mesh points to ensure the stability of the point which had been treated in the suggested style. Numerical results obtained by using these schemes are compared with existing analytical results. Excellent agreement was found between the exact solution and approximate solutions obtained by these schemes. The obtained approximate numerical solutions maintain good accuracy compared with exact solution specially for small values of the viscosity parameter.
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