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Algorithms for the fractional calculus: A selection of numerical methods

JOURNAL ARTICLE published February 2005 in Computer Methods in Applied Mechanics and Engineering

Authors: K. Diethelm | N.J. Ford | A.D. Freed | Yu. Luchko

https://doi.org/10.1016/j.cma.2004.06.006 Actions

Multi-order fractional differential equations and their numerical solution

JOURNAL ARTICLE published July 2004 in Applied Mathematics and Computation

Authors: Kai Diethelm | Neville J Ford

https://doi.org/10.1016/s0096-3003(03)00739-2 Actions

Error estimates of a high order numerical method for solving linear fractional differential equations

JOURNAL ARTICLE published April 2017 in Applied Numerical Mathematics

Authors: Zhiqiang Li | Yubin Yan | Neville J. Ford

https://doi.org/10.1016/j.apnum.2016.04.010 Actions

Pitfalls in fast numerical solvers for fractional differential equations

JOURNAL ARTICLE published February 2006 in Journal of Computational and Applied Mathematics

Authors: Kai Diethelm | Judith M. Ford | Neville J. Ford | Marc Weilbeer

https://doi.org/10.1016/j.cam.2005.03.023 Actions

An efficient parallel algorithm for the numerical solution of fractional differential equations

JOURNAL ARTICLE published September 2011 in Fractional Calculus and Applied Analysis

Authors: Kai Diethelm

https://doi.org/10.2478/s13540-011-0029-1 Actions

Numerical analysis of an operational Jacobi Tau method for fractional weakly singular integro-differential equations

JOURNAL ARTICLE published November 2017 in Applied Numerical Mathematics

Authors: P. Mokhtary

https://doi.org/10.1016/j.apnum.2017.06.010 Actions

Error analysis and approximation of Jacobi pseudospectral method for the integer and fractional order integro-differential equation

JOURNAL ARTICLE published January 2022 in Applied Numerical Mathematics

Authors: Avinash Kumar Mittal

https://doi.org/10.1016/j.apnum.2021.09.005 Actions

A numerical method for the fractional Schrödinger type equation of spatial dimension two

JOURNAL ARTICLE published June 2013 in Fractional Calculus and Applied Analysis

Authors: Neville J. Ford | M. Manuela Rodrigues | Nelson Vieira

https://doi.org/10.2478/s13540-013-0028-5 Actions

Local H1-norm error analysis of a mixed finite element method for a time-fractional biharmonic equation

JOURNAL ARTICLE published March 2022 in Applied Numerical Mathematics

Authors: Chaobao Huang | Na An | Hu Chen

https://doi.org/10.1016/j.apnum.2021.12.004 Actions

Fractional boundary value problems: Analysis and numerical methods

JOURNAL ARTICLE published December 2011 in Fractional Calculus and Applied Analysis

Authors: Neville J. Ford | M. Luísa Morgado

https://doi.org/10.2478/s13540-011-0034-4 Actions

Numerical analysis for distributed-order differential equations

JOURNAL ARTICLE published March 2009 in Journal of Computational and Applied Mathematics

Authors: Kai Diethelm | Neville J. Ford

https://doi.org/10.1016/j.cam.2008.07.018 Actions

Error analysis of spectral method for the space and time fractional Fokker—Planck equation

BOOK CHAPTER published March 2013 in Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis

Authors: Tinggang Zhao | Haiyan Xuan

https://doi.org/10.1142/9789814436465_0005 Actions

Fractional-Compact Numerical Algorithms for Riesz Spatial Fractional Reaction-Dispersion Equations

JOURNAL ARTICLE published June 2017 in Fractional Calculus and Applied Analysis

Authors: Hengfei Ding | Changpin Li

https://doi.org/10.1515/fca-2017-0038 Actions

Error estimates for an operator-splitting method for incompressible flows

JOURNAL ARTICLE published October 2004 in Applied Numerical Mathematics

Authors: J. Blasco | R. Codina

https://doi.org/10.1016/j.apnum.2004.02.004 Actions

Error estimate for the numerical solution of fractional reaction–subdiffusion process based on a meshless method

JOURNAL ARTICLE published May 2015 in Journal of Computational and Applied Mathematics

Authors: Mehdi Dehghan | Mostafa Abbaszadeh | Akbar Mohebbi

https://doi.org/10.1016/j.cam.2014.11.020 Actions

Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis

JOURNAL ARTICLE published January 2015 in Applied Mathematics and Computation

Research funded by Natural Foundation of Hebei Province (A2012203407) | Qinhuangdao Research and Development Program of Science and Technology (201201B019) | Qinhuangdao Technology Bureau 2013 (201302A023)

Authors: Yiming Chen | Xiaohong Ke | Yanqiao Wei

https://doi.org/10.1016/j.amc.2014.11.079 Actions

A finite element method for time fractional partial differential equations

JOURNAL ARTICLE published September 2011 in Fractional Calculus and Applied Analysis

Authors: Neville J. Ford | Jingyu Xiao | Yubin Yan

https://doi.org/10.2478/s13540-011-0028-2 Actions

Integration pointwise pollution error estimates in the finite element method in one dimension

JOURNAL ARTICLE published November 2004 in Applied Numerical Mathematics

Authors: G. Tsamasphyros | S. Markolefas

https://doi.org/10.1016/j.apnum.2004.01.012 Actions

Error analysis for a second order scheme for the Navier–Stokes equations

JOURNAL ARTICLE published July 2004 in Applied Numerical Mathematics

Authors: Florentina Tone

https://doi.org/10.1016/j.apnum.2003.12.003 Actions

BDF-type shifted Chebyshev approximation scheme for fractional functional differential equations with delay and its error analysis

JOURNAL ARTICLE published August 2017 in Applied Numerical Mathematics

Research funded by Government of the Russian Federation (02.A03.21.0006)

Authors: V.G. Pimenov | A.S. Hendy

https://doi.org/10.1016/j.apnum.2017.03.013 Actions
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