Alternating Direction Implicit Orthogonal Spline Collocation Methods for Solving Initial/Boundary Value Problems

摘要

The primary focus of this project was on the analysis and development of new parallel algorithms for the solution of linear and nonlinear initial/ boundary value problems (IBVPs) in two space variables. Parabolic, second order hyperbolic, biharmonic, and Schrodinger type problems were considered. The new algorithms, which are alternating direction implicit (ADI) orthogonal spline collocation (OSC) methods employing C1 piecewise polynomial spaces of arbitrary order, have been implemented and their efficacy was demonstrated on test problems taken from the literature. Rigorous stability and convergence analyses of the methods were also carried out.