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.

我们提出了一种基于B样条的半解析技术来求解2D对流扩散反应方程。所提出的技术的主要特征是将边界条件和椭圆偏微分方程的条件满足分开。更精确地说，我们将原始方程转换为具有齐次边界条件的问题，并寻求近似解作为满足问题齐次边界条件的修正B样条张量积的总和。该方法的框架中使用了三次和五次B样条。确定线性组合的系数以满足控制方程式。