Mohamed Al-Sultani

Citation

Thesis Title
Monotone iterative methods for solving nonlinear partial differential equations

Partial differential equations play a major role in the modelling of many processes which arise in physics, chemistry and engineering. Most of these partial differential equations cannot be solved analytically and classical numerical methods are not always applicable. Thus, efficient and stable numerical approaches are needed. For solving coupled systems of elliptic and parabolic equations, Mr Al-Sultani constructed and investigated block monotone Jacobi and Gauss-Seidel iterative methods. He estimated the errors between the numerical solution and the exact solution of the nonlinear difference schemes and the corresponding continuous problems. He found out that the block monotone methods converge faster than the corresponding point monotone methods. He applied the developed numerical methods to the gas-liquid interaction model and the Volterra-Lotka competition model in ecology.

Supervisors
Professor Igor Boglaev
Associate Professor Tammy Lynch