Time integrations in solution of diffusion problems by local integral equations and moving least squares approximation

摘要

The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulation for local integral equations is employed. A comparative study of numerical results obtained by the Laplace transform and the time stepping approach is given in a test example for which the exact solution is available and utilized as a benchmark solution.