[00032] A geometrically preservative semi-adaptive method for the numerical solution of Kawarada equations
Session Time & Room : 1E (Aug.21, 17:40-19:20) @E702
Type : Contributed Talk
Abstract : This presentation concerns the numerical stability and geometric preservations of the numerical
solution of Kawarada equation problems. The nonlinear partial differential equations
exhibit strong quenching types of singularities that represent a number of key characteristics
from industrial and multi-physical applications. A second order semi-adaptive implicit finite difference
method will be constructed and investigated. We shall begin with a detailed mathematical analysis of the
stability without freezing singular source terms of Kawarada equations in this talk.
Preservation features of the solution vector sequences will then be
studied. Realistic orders of the convergence will be given via generalized Milne's devices. Finally,
computer simulations will be carried out to demonstrate the effectiveness of the
theoretical analysis and conclusions.
