解分数阶Endolymph微分方程的一些技巧

Abstract

考虑分数阶Endolymph微分方程,证明了其解的存在性与惟一性.利用拉普拉斯变换及其逆变换求出了用格林函数表示分数阶Endolymph微分方程的解析解.作者提出一种计算有效的方法,即预估-校正方法,可求出它的数值解.最后给出了数值例子来说明这个预估-校正方法是模拟分数阶Endolymph微分方程解性态的计算有效的方法.这个数值技巧可以应用于模拟其它分数阶的常微分方程.

The fractional differential equations of Endolymph is considered.The existence and uniqueness of solution for the fractional differential equations of Endolymph is proved.Using Laplace and its inverse transformation,the analytical solution of the fractional differential equations of Endolymph is derived by the corresponding Green's function.A computationally effective method,Predictor-Corrector method,is proposed for solving the fractional differential equations of Endolymph for its numerical solutions.Finally,we give some numerical examples to show that the Predictor-Corrector method provides a computational effective method for simulating the behavior of the solution of the fractional differential equations of Endolymph.This numerical technique can be applied to simulate other fractional ordinary differential equations.