We describe a symbolic-numerical method for the Fourier stability analyses of difference initial-value problems approximating the initial-value problems for hyperbolic or parabolic PDEs. The Fourier method is reduced to the algebra of the resultants. We further use the REDUCE computer algebra...

Stability is one of the important properties of time-stepping numerical schemes that are used to approximate partial differential equations. Stability can be analyzed using Von Neumann stability analysis which is a Fourier method. The analysis results in the Von Neumann stability condition which...

We compare classical methods for singular perturbation problems, such as El-Mistikawy and Werle scheme and its modifications, to exponential spline collocation schemes. We discuss subtle differences that exist in applying this method to one dimensional reaction–diffusion problems and...