Mesh-free methods and time integrations for transient heat conduction

The paper deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various mesh free approximations,while the time dependence is treated either by the Laplace transform method and/or by the polynomialinterpolation in the time stepping method. The accuracy and convergence of the numerical results as well as the computational e?ciency of various approaches are compared in numerical test example.