The Alternating-Triangular Algorithm for the Analysis of Blow-Up and Quenching Phenomena in Nonlinear PDEs

Melnik, R.V.N.

International Journal of Mathematical Algorithms, 2, 89-120, 2000

Abstract:

The author applies an effective numerical method for the solution of 2-D nonlinear parabolic and elliptic equations, which describe a wide range of phenomena from physics, chemistry, biology and economics. For instance, reaction-diffusion problems, models for heat localization, flame propagation and semiconductor devices. The effectiveness of the method for the problems with fast-changing coefficients as well as different types of nonlinearities are demonstrated. Blow-up and quenching phenomena are studied using the software package ALTPACK that makes use of the alternating-triangular method with ordered Chebyshev set of iterative parameters. The results of computational experiments on the blow-up and quenching phenomena are presented.