基于二次样条插值函数,对常系数对流扩散方程提出了一种最优紧配置法.首先在空间方向利用二次样条基函数进行离散,使得问题化为时间方向的一系列常微分方程组;然后,利用Runge-Kutta方法、梯形公式法进行迭代求解,并且在实验中比较、分析了此类配置法在使用Runge-Kutta方法和梯形公式法迭代求解时的数值稳定性.结果表明,在时间方向无论使用哪种迭代法,此配置法在空间方向均可达到4阶精度.%Based on the quadratic spline interpolation functions, an optimal compact quadratic spline collocation method is presented for the convection-diffusion equation.As for The said method, first by use of quadratic spline basis function, discretization is done in the space direction, thus the problem is transformed into a series of ordinary differential equation.Then, the classical fourth-order Runge-Kutta method and Trapezoid formula are respectively employed to determine the iterative solution and with experiments the numerical stability of the method is compared and analyzed.Numerical examples find that the presented collocation scheme can achieve fourth-order accuracy in space no matter which kind of iterative method is used.
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