On an Approximation Model via Galerkin Method for a Parabolic Distributed Parameter System with Boundary Inputs

Abstract

For a parabolic distributed parameter system with boundary inputs, we consider a finite dimensional approximation scheme of Galerkin type and propose a method yielding approximation models with no static errors.
We illustrate a modal interpretation of the approximation model in the caseeigenfunction is employed for the coordinate function and show that the magnitude of the approximation errors of the higher order modes are proportional to the first-order differential of the system input.
We verify above results numerically both by simulation study in time domain and error evaluation in frequency domain, for an example of a constant parameter system.