佐々木 多希子

This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method. (C) 2016 Elsevier B.V. All rights reserved.

Finite-difference schemes for computing blow-up solutions of one dimensional nonlinear wave equations are presented. By applying time increments control technique, we can introduce a numerical blow-up time which is an approximation of the exact blowup time of the nonlinear wave equation. After having verified the convergence of our proposed schemes, we prove that solutions of those finite-difference schemes actually blow up in the corresponding numerical blow-up times.Then, we prove that the numerical blow-up time converges to the exact blow-up time as the discretization parameters tend to zero.Sev eral numerical examples that confirm the validity of our theoretical results are also offered.