Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

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