用积分算子方法求二阶数值微分

Solve Second-order Numerical Differentiation by Using Integral Operator

数值微分就是用离散方法近似地求出函数在某点的导数值。关于数值微分己有许多求解方法,但这些方法都有各自的局限性,且关于二阶导数近似逼近的方法研究相对较少。基于Groetsch的思想,提出了利用积分算子来构造近似二阶导数的方法,并将此方法应用于二阶数值微分问题,给出了相应的误差估计。通过数值实验表明,此方法对于二阶数值微分问题十分有效,而且计算量小。

Numerical differentiation was that derivative value of a function at a certain point was approximately solved in discrete method.There have been a lot of solutions to numerical differentiation.However,they have their limitations of their own.Moreover,there were relatively few researches on derivative of second order approximation.Based on Groetsch＇s thought a method was brought forward that could structure approximate second-order derivative by using integral operator and by applying it to second-order numerical problems we provide corresponding error estimate.It was made clear by numerical experiments that the method was much valid to second-order numerical differential problems;what＇s more there were not many calculations.