Last Wednesday, Dr Joseph Kolibal from the Department of Mathematics give us a lecture on the numerically solution of Partial Deferential Equations by applying Mollifyers.

Dr. Kolibal first gave the introduction of the problem. Approximations of functional derivatives are constructed through a process of mollification. The resultant functional approximations are analytic and are suitable for numerically solving partial differential equations. Since the derivatives are obtained analytically from a smooth approximation of the function, all derivatives at a point are available at any location in the domain during the numerical differentiation.

Dr. Kolibal discussed the techniques applied to filtering noisy function g. Thesecan be subsumed within the theory of mollifier. Dr. Kolibal also discussed the one dimensional model, two dimensional system of equations, and discretization problems.