Author(s)

Okey Oseloka Onyejekwe

Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa, Ethiopia.

It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a sys-tem of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.

Boundary Element Method, Green’s Identity, Complementary Equation, Fundamental Solution, Hybrid Formulation, Integro-Differential Transport Equation

Onyejekwe, O. (2016) A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory. Applied Mathematics, 7, 1241-1247. doi: 10.4236/am.2016.711109.