Open Access
2019 A hybrid collocation method for fractional initial value problems
Linjun Wang, Fang Wang, Yanzhao Cao
J. Integral Equations Applications 31(1): 105-129 (2019). DOI: 10.1216/JIE-2019-31-1-105


This paper is concerned with the application of a hybrid collocation method to a class of initial value problems for differential equations of fractional order. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with a weakly singular kernel. Then, the Volterra integral equation is converted to a fixed point problem. A hybrid collocation algorithm is developed to solve the fixed point problem, and the optimal order of convergence of the proposed algorithm is obtained. Two numerical experiments are conducted to demonstrate the efficiency of the hybrid collocation algorithm.


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Linjun Wang. Fang Wang. Yanzhao Cao. "A hybrid collocation method for fractional initial value problems." J. Integral Equations Applications 31 (1) 105 - 129, 2019.


Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07080017
MathSciNet: MR3974985
Digital Object Identifier: 10.1216/JIE-2019-31-1-105

Primary: 26A33 , 45G10 , 65L05

Keywords: convergence order. , Fractional initial value problem , hybrid collocation method , weakly singular kernel

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

Vol.31 • No. 1 • 2019
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