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In this paper, we devise three finite difference methods in order to solve a 1-D Korteweg-de-Vries Burger's (KdVB) equation with specified initial and boundary conditions. The test case is taken from [6] and the exact solution is known for this problem. We obtain the stability region and compare the performance of our three methods with the sinc-collocation method [6] by computing L∞, L2 errors at some different times and also obtain absolute errors and relative errors at some spatial nodes. [ABSTRACT FROM AUTHOR]

In this work, three finite difference methods have been used to solve a three dimensional advection-diffusion equation with given initial and boundary conditions. The three methods are fourth order finite difference method, Crank-Nicolson and Implicit Chapeau Function. We compare the performance of the methods by computing L2 error, L∞ error and some performance indices such as mass distribution ratio (MDR), mass conservation ratio (MCR), total mass and R² which is a measure of total variation in particle distribution. [ABSTRACT FROM AUTHOR]

In this paper, three numerical methods have been used to solve a 1-D Convection-Diffusion equation with specified initial and boundary conditions. The methods used are the third order upwind scheme [1], fourth order upwind scheme [1] and a Non-Standard Finite Difference (NSFD) scheme [4]. The problem we considered has steep boundary layers near x = 1 [3] and this is a challenging test case as many schemes are plagued by nonphysical oscillation near steep boundaries. We compute the L2 and L∞ errors, dissipation and dispersion errors when the three numerical schemes are used and observe that the NSFD is much better than the other two schemes for both coarse and fine grids and also at low and high Reynolds numbers. [ABSTRACT FROM AUTHOR]