Error estimates for multiwavelet approximations of a class of history dependent operators

摘要

This paper presents a multiwavelet approximation technique for a class of history dependent operators. The study is motivated by increasing interest in estimation and control techniques for dynamical systems whose governing equations include history dependent nonlinearities. The functional differential equations in this paper are constructed using integral operators that depend on distributed parameters. We derive the rate of convergence of finite dimensional approximations to the infinite dimensional model as a function of mesh resolution for the history dependent operators in this paper. We also study a collection of predictor-corrector integration methods that can attain the convergence rates derived for the history dependent operators in this paper, provided that certain smoothness conditions apply.