求解常微分方程的函数逼近法

Function approximation method to solve the ordinary differential equations

提出了一种利用函数逼近法求解常微分方程(ODE)初值问题的数值方法。在多项式空间中寻找函数,在某种距离意义下尽可能满足微分方程,从而获得微分方程的近似解。通过理论分析可知,求解常微分方程的欧拉法、梯形法是该方法的特例,数值试验进一步表明了该方法的有效性。

A numerical function approximation method is proposed to solve the ordinary differential equations （ODE） initial value problems. The method intends to seek a function which meets the differential equation as far as possible in the polynomial space, so as to obtain the approximate solution of the differential equation. It can be proved that the solution of ordinary differential equation of Euler method, trapezoidal method is a special case of this method. Numerical test further shows the effectiveness of the method.