带Neumann边界条件的抛物型方程的样条差分方法Spline Difference Method for Solving Parabolic Equations with Neumann Boundary Conditions
刘蕤,高锐敏
摘要(Abstract)：
基于四次样条函数和广义梯形公式,针对抛物型方程的Neumann边值问题,构造了一族含参数θ(θ∈[0,1])的隐式差分格式,该格式在时间方向的精度为二阶,在空间方向的精度为四阶,当θ=1/3时,该差分格式在时间方向的精度可提高到三阶.数值实验表明方法是非常有效的.
关键词(KeyWords)： 抛物型方程;四次样条函数;差分格式;Neumann边值问题
基金项目(Foundation): 河南省基础与前沿技术研究计划项目,编号132300410381
作者(Author): 刘蕤,高锐敏
参考文献(References)：
- [1]金承日.解抛物线型方程的高精度显示差分格式[J].计算数学,1991,13(1):38-44.
- [2]马明书.一维抛物线方程的一个新的高精度显示差分格式[J].数值计算与计算机应用,2001,22(2):156-160.
- [3]刘利斌,刘焕文.一维抛物线方程的样条子域精细积分(SSPI)隐格式[J].数值计算与计算机应用,2008,29(2):146-152.
- [4]杨国锋,李波,田巧娴,等.求解一维抛物型方程的一种高精度半显示差分方法[J].西北师范大学学报:自然科学版,2008,44(3):8-11.
- [5]詹涌强.解抛物型方程的一族六点隐式差分格式[J].安徽大学学报:自然科学版,2012,36(4):26-29.
- [6]Caglar H,Ozer M,Caglar N.The numerical solution of the one-dimensional heat equation by using third degree B-spline func-tions[J].Chaos Solitons Fractals,2008,38(4):1197-1201.
- [7]Sun Zhizhong.Compact difference schemes for heat equation with Neumann boundary conditions[J].Numerical Methods Partial Differential Equation,2009,25(6):1320-1341.
- [8]Chawla M,Zanaidi M A,Evans D J.Generalized trapezoidal formulas for parabolic equations[J].Intentional Journal of Com-puter Mathematics,1999,70(3):429-443.
- [9]Sallam S,Karaballi A A.A quartic C 3-spline collocation method for solving second-order initial value problems[J].Journal of Computational and Applied Mathematics,1996,75(2):295-304.
- [10]Liu Huanwen,Liu Libin.An unconditionally stable spline difference scheme of O(k 2+h 4)for solving the second-order1D linear hyperbolic equation[J].Mathematical and Computer Modelling,2009,49(9/10):1985-1993.
- [11]Liu Libin,Liu Huanwen.A new fourth-order difference scheme for solving an N-carrier system with Neumann boundary condi-tions[J].International Journal of Computer Mathematics,2011,88(6):3553-3564.