2014 年 5 巻 3 号 p. 320-338
We consider the methods for guaranteed computations of solutions for nonlinear parabolic initial-boundary value problems. First, in order to make the basic principle clear, we briefly introduce the numerical verification methods of solutions for elliptic problems which we have developed up to now. Next, under some fundamental procedures of verification for parabolic problems based on the fixed point theorem with Newton's method, we describe a summary of our methods including additional new technique which could yield some improvements. The main contents of the paper consist of the guaranteed a posteriori estimates for the linearized inverse operators of parabolic type. In order to confirm the effectiveness of our methods, we give some numerical examples for the guaranteed bounds of iverse operators as well as give some prototype results for numerical verification of solutions of nonlinear parabolic problems. Moreover, we will mention an extention of the present technique to the verification of time-periodic solutions.
