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

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.

Based on the quartic spline function and generalized trapezoidal formulas, a family of implicit difference schemes, including parameter 0, 0 E [0, 1 ], for solving parabolic equation with Neumann boundary conditions were constructed. The accuracy of these schemes was second-order in time direction and fourth-order in space direction. If 0 = 1/3, the accuracy of this scheme in time direction was im- proved to third-order. At last, the numerical results showed that our methods were very efficient.