Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

Angelamaria Cardone, Dajana Conte, Raffaele D’Ambrosio and Beatrice Paternoster
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Angelamaria Cardone: Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
Dajana Conte: Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
Raffaele D’Ambrosio: Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy
Beatrice Paternoster: Department of Mathematics, University of Salerno, 84084 Fisciano, Italy

Mathematics, 2022, vol. 10, issue 2, 1-17

Abstract: The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

Keywords: ordinary differential equations; fractional differential equations; multistep methods; collocation; convergence; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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