A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

We present a B-spline based semi-analytical technique for solving 2D convection-diffusion-reaction equations. The main feature of the presented technique is to separate the satisfaction of the conditions on the boundary and the elliptic partial differential equation inside. To be more precise, we transform the original equation into the problem with homogeneous boundary conditions and seek the approximate solution as a sum of the modified B-spline tensor products which satisfy the homogeneous boundary conditions of the problem. The cubic and quintic B-spline are used in the framework of the method. The coefficients of linear combination are determined to satisfy the governing equation. Eight numerical examples have been studied to demonstrate the high effectivity of the presented technique in solving 2D convection-diffusion-reaction problems in single and multi-connected domains.