Abstract—A semi-analytic integration method to handle the singularity of a parametrix concerning of direct united boundary-domain integro-differential Equation (BDIDE) related to the dirichlet boundary value problem for an elliptic Partial Differential Equation (PDE) with variable coefficient is presented in this paper. This approach can be an alternative to the Gauss-Laguerre quadrature formula to evaluate the integration with a kernel that deals with logarithmic singularity. The development of this method is inspired by the fact that the exact solution of an integral moves faster than its numerical solution. By using this approach, a result with high accuracy can still be obtained even with minimize numbers of the Gaussian quadrature points and thus reduce the numerical effort in the numerical integration.

Index Terms—Direct united boundary-domain integro-differential equation, Dirichlet problem, partial differential equation, semi-analytic integration method.

N. A. Mohamed is with the Mathematical Department, Faculty of Science and Mathematics, Sultan Idris Education University (UPSI), 35900 Tanjong Malim, Perak Darul Ridzuan, Malaysia (e-mail: akmal.mohamed@fsmt.upsi.edu.my).

Cite: N. A. Mohamed, "Semi-Analytic Integration Method for Direct United Boundary-Domain Integro-Differential Equation Related to Dirichlet Problem," International Journal of Applied Physics and Mathematics vol. 4, no. 3, pp. 149-154, 2014.