Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1118.65079
Lin, R.; Liu, F.
Fractional high order methods for the nonlinear fractional ordinary differential equation. (English)
[J] Nonlinear Anal., Theory Methods Appl. 66, No. 4, A, 856-869 (2007). ISSN 0362-546X

The paper begins by referring to applications of fractional order equations, along with a brief summary of the main results achieved for this type of equation in the last decade. The authors consider the nonlinear fractional-order order differential equation (NFOODE), $_0D_t^\alpha y(t)=f(y,t), (t>0), n-1<\alpha \le n, y^{(i)}(0)=y_0^{(i)}, i=0, 1, 2,\dots, n-1$ where $f(y,t)$ satisfies the condition $\vert f(y_1,t)-f(y_2,t)\vert \le L\vert y_1-y_2\vert $ in $t\in [0,T]$. Existence and uniqueness theorems for the NFOODE, by {\it K. Diethelm} and {\it N. J. Ford} [J. Math. Anal. Appl. 265, No. 2, 229--248 (2002; Zbl 1014.34003)], are stated. High order fractional linear multi-step methods ($p$-HOFLMSM) are introduced. Definitions pertaining to their consistency and stability are stated. New results relating to the consistence, convergence and stability of these methods are presented and proved. The paper concludes with numerical examples which demonstrate the computational efficiency of the $p$-HOFLMSM.
[Pat Lumb (Chester)]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
65L20 Stability of numerical methods for ODE
26A33 Fractional derivatives and integrals (real functions)
34K28 Numerical approximation of solutions of FDE
34A34 Nonlinear ODE and systems, general
65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: fractional order methods; nonlinear fractional order equations; consistency; convergence; stability; fractional linear multi-step methods; numerical examples

Citations: Zbl 1014.34003

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]