Trapezoidal methods for fractional differential equations: theoretical and computational aspects

Abstract

The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical experiments are provided to illustrate potential and limitations of the different methods under investigation.

References in corpus (2)

• On an explicit finite difference method for fractional diffusion equations
• A Finite Difference Method with Non-uniform Timesteps for Fractional Diffusion Equations

Cited by in corpus (20)

• Fractional Calculus in Pharmacokinetics
• Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations
• A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
• Upper and lower estimates for the separation of solutions to fractional differential equations
• Efficient computation of the Wright function and its applications to fractional diffusion-wave equations
• A constructive approach for investigating the stability of incommensurate fractional differential systems
• A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials
• A new approach to shooting methods for terminal value problems of fractional differential equations
• Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
• Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems
• Fast IMEX Time Integration of Nonlinear Stiff Fractional Differential Equations
• Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay
• A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method
• FdeSolver: A Julia Package for Solving Fractional Differential Equations
• Analysis and implementation of collocation methods for fractional differential equations
• Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type
• A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations
• A shooting-Newton procedure for solving fractional terminal value problems
• Mittag--Leffler stability of numerical solutions to time fractional ODEs
• Abstract Fractional Cauchy Problem: Existence of Propagators and Inhomogeneous Solution Representation