Application of the method of weighted residuals to mixed (split) boundary value problems. Triple series equations

Abstract

The method of weighted residuals is applied as a means of providing approximate solutions to mixed (split) boundary value problems which are described by triple-series relations. This approach relies upon using the triple series kernel as the basis function and results in a linear system of equations with the series coefficients as the unknowns. Any available method such as LU decomposition or Gaussian elimination is then used to solve this system. The approach developed in this study is illustrated by numerical examples for diffusion and reaction which are solved using a special software package which implements the proposed algorithms.