Neumann问题热平衡积分法细化解的收敛性  

Convergence Properties of the Refined Heat Balance Integral Solution for the Neumann Problem

作　　者：徐湘田[1,2] 令锋[2] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]肇庆学院计算机科学与软件学院,肇庆526061

出　　处：《工程数学学报》2010年第3期503-512,共10页Chinese Journal of Engineering Mathematics

基　　金：广东省自然科学基金(04011600);教育部留学回国人员科研启动基金([2005]55)~~

摘　　要：本文应用热平衡积分法及其细化方法求得了Neumann问题的分段线性近似解。在参数S充分大的条件下,应用伽玛函数及不完全伽玛函数的性质,证明了Neumann问题的热平衡积分细化解的收敛性,并求得各相的收敛速度分别为O(n-1)、O(n-1/2)。本文推广了热平衡积分细化解收敛性分析中的一些已知结论。A piecewise linear approximate solution for the Neumann problem is presented by using the heat balance integral method and its refined method. It is proved that the approximate solution converges formally to the exact solution at large values of the parameter S and the convergence rate in each phase is O（n-1） and O（n-1/2）, respectively, by using the properties of the Gamma function and incomplete Gamma function. The methods used in this paper can be applied to two-phase and multi-phase heat conduction problems. The present work generalizes the former results in convergence analysis to the refined heat balance integral solution.

关 键 词：热平衡积分法 近似解 NEUMANN问题 收敛速度 

分 类 号：O175.29[理学—数学]