线性高振荡微分方程在两组不同基下的近似解

Approximating Solution to Highly-oscillatory Linear Differential Equation

分别以Bernstain多项式以及准均匀B样条为基函数,来逼近线性高振荡常微分方程。通过求解基函数对应的系数方程组,得到方程的近似解。通过数值实验表明用准均匀B样条函数的逼近效果要比Bernstain多项式要好。

This paper deals with approximating solutions to highly- oscillatory linear differential equations in Bernstain polynomial basis and quasi - uniform B- spline separately. We solve the equations of coefficients to get the numerical solution and by numerical experimentation we can see that the solutions in quasi - uniform B - spline basis is better than those in Bernstain polynomial basis.