  As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct
Meshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical
solution of transient heat conduction problem. The new technique is based on
direct recoveries of test functionals (local weak forms) from values at nodes
without any detour via classical moving least squares (MLS) shape functions.
This leads to an absolutely cheaper scheme where the numerical integrations
will be done over low-degree polynomials rather than complicated MLS shape
functions. This eliminates the main disadvantage of MLS based methods in
comparison with finite element methods (FEM), namely the costs of numerical
integration.
