关键词: 光滑余因子协调法, 四次 B 样条, 对流-扩散方程, 有限差分法, 微分方程数值解

Abstract: Based on the quartic B spline function, a quartic B spline method for solving a class of convection-diffusion equations was presented. By means of the conformality of smoothing cofactor method, univariate quartic B spline bases were firstly obtained over uniform knots. Secondly, representations of B splines were calculated at the endpoints with multiple knots on the bounded closed interval. In addition, all the quartic B spline bases possessed good properties, such as non-negative property and partition of unity. Thirdly, univariate quartic B spline functions were applied in solving a class of one-dimensional convection-diffusion equations, where discrete in time was realized by forward finite differences and discrete in space was by quartic spline approximation with the parameter δ introduced. Then the convection-diffusion equation was solved by the quartic B spline functions. Finally, according to the numerical example, the comparison was made between the quartic spline approximation method and the finite difference method, and an intuitive comparison of numerical errors was given, which indicates that the former is more convenient and practical than the latter.

Key words: conformality of smoothing cofactor method, quartic B-spline, convection-diffusion equation, finite difference method, numerical solution of differential equation