This work presents the development and testing of time integration schemes for the system of ordinary differential equations resulting from the Dual Reciprocity Boundary Element Method (DRM/BEM) for the transient diffusion and convection-diffusion equations. The article describes applications of two-level and three-level schemes and the numerical solutions are compared with available analytical solutions for different combinations of the time step numerical weighting factors. Also, a method is proposed based on the three-level scheme together with active polynomial Richardson extrapolation of the solution. This method is particularly recommended for problems that require very high accuracy such as long term simulations. Results demonstrate that the proposed method is more economic in computer time and gives more accurate results than the two and three-level schemes.
