Numerical solution of singular BVPs in ODEs and parabolic PDEs using collocation.

Abstract

The main part of this work covers the solution of initial-/boundary value problems of parabolic differential equations. A code for the solution of boundary value problems of ordinary differential equations using collocation is utilized to achieve that. Discretization in time yields a boundary value problem in space for each time step. The boundary value problem gets solved, trying to control step widths in time to satisfy both time and space tolerances. This way the parabolic differential equation can be solved numerically. The Matlab solver is then used for some test problems. To increase the efficiency of the solver a grid adaptation algorithm is developed to improve the performance of the solution of the boundary value problems. Furthermore boundary value problems of different applications will be solved and documented.