 Numerical approximation for a nonlinear variable-order fractional differential equation via a collocation methodXiangcheng Zheng Mathematics and Computers in Simulation (MATCOM), 2022, vol. 195, issue C, 107-118 Abstract: We study a numerical approximation for a nonlinear variable-order fractional differential equation via a collocation method. Due to the lack of monotonicity of the discretization coefficients of the variable-order fractional derivative in standard approximation schemes, existing numerical analysis techniques do not apply directly. By an approximate inversion technique, the proposed model is transformed as a second kind Volterra integral equation, based on which a collocation method under uniform or graded mesh is developed and analyzed. In particular, the mesh grading parameter we used is consistent with respect to the regularity of the solutions, and the convergence rates are characterized in terms of the initial value of the variable order, which serve as improvements compared with the existing results in the literature. Keywords: Nonlinear fractional differential equation; Variable-order; Collocation method; Graded mesh; Error estimate; Integral equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:195:y:2022:i:c:p:107-118 DOI: 10.1016/j.matcom.2022.01.005 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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