对流-扩散方程的样条子域精细积分隐格式  

Spline Sub-Domain Precise Integration Implicit Scheme for Solving Convection-Diffusion Equation

作　　者：徐金平[1] 单双荣[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2009年第5期590-592,共3页Journal of Huaqiao University(Natural Science)

基　　金：国务院侨办科研基金资助项目(04QZR09)

摘　　要：针对对流-扩散方程的初边值问题,利用子域精细积分的思想,结合三次样条函数逼近,提出含参数(α>0)的一族无条件稳定的隐格式,其局部截断误差阶为O(ατ+τ2+h2).当参数0<α≤τ时,其精度相当于O(τ2+h2),且可用三对角线追赶法容易地求解.数值计算表明,理论分析与实际例子相符合.Based on sub-domain precise integration method and combined the cubic spline function approximation, a double-layer impllicit scheme containing parameter α〉0 for the initial-boundary value problem of convection-diffusion equation is presented. It is shown that this implicit scheme is unconditionally stable, and the order of local truncation error of the present method is O（ατ＋τ^2＋h^2）. When the parameter satisfies 0〈α≤τ, the order of local truncation error equals to O（τ^2＋h^2） which can be simply solved by triple diagonal pursuit method. The numerical calculus is consistent with theoretical analysis.

关 键 词：对流-扩散方程 样条函数 子域精细积分 稳定性 隐格式 

分 类 号：O241.82[理学—计算数学]