一类运动学问题数值解的快速实现

A Fast Realization of Numerical Solutions for a Class of Kinematics Problems

以一个可转化为求解初值条件下解常微分方程的运动学问题为例,给出该问题下采用Euler法、改进Euler法以及Runge-Kutta法的具体格式,利用基本办公软件Execl的迭代计算及循环迭代计算功能给出三种格式下该问题的较高精度近似数值解和误差对比,利用绘图软件OriginPro8.0将数值拟合成相应曲线以使对比更直观.通过对比说明,各数值法在一定精度要求范围内能给出符合实际要求的结果.将数值法与Execl迭代计算功能结合使用,给解决实际物理问题带来较大的便利性.

An example of kinematics problem,which can be converted into the problem of solving ordinary differential equations under initial conditions was used as a demo case,and the concrete formats of this problem when adopting the Euler method,improved Euler method and runge-kutta method were put forth.By use of the iterative calculation of basic office software of EXCEL and the loop iteration calculation function,the approximate numerical solution with a relatively high accuracy to this problem and the error comparison under the three formats were presented,and then by aid of the drawing software OriginPro8.0 the numerical values were synthesized into a numerical fitting curve so that it is made to be visually more intuitive.By comparison,each numerical method can produce,within the range of certain accuracy,the results that can meet the actual demands.Combining the numerical method with the EXCEL iterative computing function,it can bring great convenience to solving practical physics problems.