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Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems

The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are approximated in terms of radial basis functions. The application of DQM for time derivative discretization when it is combined with the DRBEM gives an overdetermined system of linear equations since both boundary and initial conditions are imposed. Then the least squares approximation is made use of for solving the overdetermined system. Thus, the solution is obtained at any time level without an iterative scheme. Numerical results are in very good agreement with the theoretical solutions of the test problems considered.