کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
844547 | 908598 | 2007 | 14 صفحه PDF | دانلود رایگان |

In this paper, we consider the nonlinear fractional-order ordinary differential equation 0Dtαy(t)=f(y,t), (t>0)(t>0), n−1<α≤nn−1<α≤n, y(i)(0)=y0(i), i=0,1,2,…,n−1i=0,1,2,…,n−1, where f(y,t)f(y,t) satisfies the LL-condition, i.e., |f(y1,t)−f(y2,t)|≤L|y1−y2||f(y1,t)−f(y2,t)|≤L|y1−y2| in t∈[0,T]t∈[0,T]. Fractional-order linear multiple step methods are introduced. The high order (2–6) approximations of the fractional-order ordinary differential equation with an initial value are proposed. The consistence, convergence and stability of the fractional high order methods are proved. Finally, some numerical examples are provided to show that the fractional high order methods for solving the fractional-order nonlinear ordinary differential equation are computationally efficient solution methods.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 66, Issue 4, 15 February 2007, Pages 856–869