Novel Integration in Time Methods via Deferred Correction Formulations and Space-Time Parallelization

A major avenue of research in numerical analysis is creating algorithms in order to decrease the amount of computational time in numerical simulations while maintaining high accuracy. Notably when modeling PDE systems, much effort has been focused in creating methods that undergo the spatial calculations very quickly and accurately. Even with these results, simulations may still take too long, limiting the robustness of a numerical model. Hence, a new research direction is to create methods that decrease runtime by focusing on the temporal direction. The subject of this dissertation is the development of algorithms that decrease runtime by taking acount of temporal properties, and when possible coupling both temporal spatial properties, of time-dependent differential equations.Doctor of Philosoph