The application of the multigrid algorithm to the solution of stiff ordinary differential equations resulting from partial differential equations.
MetadataShow full item record
We wish to apply the newly developed multigrid method  to the solution of ODEs resulting from the semi-discretization of time dependent PDEs by the method of lines. In particular, we consider the general form of two important PDE equations occuring in practice, viz. the nonlinear diffusion equation and the telegraph equation. Furthermore, we briefly examine a practical area, viz. atmospheric physics where we feel this method might be of significance. In order to offer the method to a wider range of PC users we present a computer program, called PDEMGS. The purpose of this program is to relieve the user of much of the expensive and time consuming effort involved in the solution of nonlinear PDEs. A wide variety of examples are given to demonstrate the usefulness of the multigrid method and the versatility of PDEMGS.
Showing items related by title, author, creator and subject.
Leach, Peter Gavin Lawrence. (1995)In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first ...
Pitts, Susan. (2015-01-05)The fractional calculus of deterministic functions is well known and widely used. Mean-square calculus is a calculus that is suitable for use when dealing with second-order stochastic processes. In this dissertation we ...
Kajotoni, Margaret Modupe. (2008)The collocation method for solving ordinary differential equations is examined. A detailed comparison with other weighted residual methods is made. The orthogonal collocation method is compared to the collocation method ...