Applied Mathematics Colloquium with Tim Sheng

Speaker: Tim Sheng, Baylor University

Title: From Decomposition to Combination – A Continuing Endeavor of the Splitting Methods.

Abstract: Splitting methods, with representative examples such as ADI (alternating-direction implicit) method and LOD (local one-dimensional) method, have been playing a significant role for the numerical solution of partial differential equations. In this talk, we will start from a seemed-to-be obvious issue as an introduction of the modern splitting methods. Historical roots of the literature will be mentioned. The concept of global error and its estimates will be discussed and explored. We will finally use a splitting approach for solving a semi-linear Kawarada partial differential equation which is extremely important

to solid fuel combustion, environmental protection, and biomedical research. Mesh adaptations will be incorporated with decompositions.

 

Applied Mathematics Colloquia