A numerical solution for advection‐diffusion equation using dual reciprocity method

This article describes a numerical method based on the boundary integral equation and dual reciprocity method(DRM) for solving the one‐dimensional advection‐diffusion equations. The concept of DRM is used to convert the domain integral to the boundary that leads to an integration free method. The time derivative is approximated by the time‐stepping method. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of the new approach. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013