Highly accurate and efficient numerical methods for a problem of heat conduction

Abstract

In this work, we present a theoretical basis for the Steklov series expansion methods to reduce and estimate the error of numerical solutions for heat conduction. The meshless spectral method is applied to represent the temperature over the two-dimensional field using the harmonic Steklov eigenfunctions. Error estimates for Steklov approximations are given. With explicit formulae for the Steklov eigenfunctions and eigenvalues, results about the accuracy of the methods for several variables of interest according to the number of eigenfunctions used are described.