Noel F. Heitmann - University of Pittsburgh
Numerical Solutions to Partial Differential Equations - An Introduction to Finite Difference Methods
Partial differential equations model a vast number of phenomena. The applications are too many to name, however they range from pollutant tracking to option pricing to nuclear engineering. Unfortunately, most PDE are not solvable by analytic means. As a consequence, a great deal of research is directed toward solving PDE numerically. In this talk, we present the basics of the finite difference approach to solving PDE. As a model, we take a simple transient convection diffusion problem in one spatial dimension. In developing a solution to the problem we do the following:
- Perform numerical analysis on the spatial approximation
- Create a system of equations that represent the problem
- Investigate the computed solution
We will also consider the issue of stability of approximate solutions. If time permits, we will present a subgrid stabilization method for the general transient convection diffusion problem and look at some numerical results.
This talk should be accessible to undergraduate math majors at the sophomore level. Students who know Taylor's Theorem and basic matrix algebra should have no trouble following the ideas presented.
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