An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

N. J. Ford; Maria Luisa Morgado; M. Rebelo

An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

N. J. Ford, Maria Luisa Morgado, M. Rebelo

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Abstract

In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.

Original language	English
Pages (from-to)	289-305
Number of pages	17
Journal	Electronic transactions on numerical analysis
Volume	44
Publication status	Published - 2015

Keywords

Caputo derivative
fractional differential equation
subdiffusion
finite difference method
distributed order differential equation
FRACTIONAL SUB-DIFFUSION
SUBDIFFUSION EQUATION
STABILITY
SCHEME

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An implicit finite difference approximation for the solution of the diffusion equation with distributed order in timeFinal published version, 5.53 MBLicence: CC BY

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title = "An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time",

abstract = "In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.",

keywords = "Caputo derivative, fractional differential equation, subdiffusion, finite difference method, distributed order differential equation, FRACTIONAL SUB-DIFFUSION, SUBDIFFUSION EQUATION, STABILITY, SCHEME",

author = "Ford, {N. J.} and {Luisa Morgado}, Maria and M. Rebelo",

note = "Sem PDF",

year = "2015",

language = "English",

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pages = "289--305",

journal = "Electronic transactions on numerical analysis",

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publisher = "KENT STATE UNIVERSITY",

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T1 - An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

AU - Ford, N. J.

AU - Luisa Morgado, Maria

AU - Rebelo, M.

N1 - Sem PDF

PY - 2015

Y1 - 2015

N2 - In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.

AB - In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.

KW - Caputo derivative

KW - fractional differential equation

KW - subdiffusion

KW - finite difference method

KW - distributed order differential equation

KW - FRACTIONAL SUB-DIFFUSION

KW - SUBDIFFUSION EQUATION

KW - STABILITY

KW - SCHEME

M3 - Article

SN - 1068-9613

VL - 44

SP - 289

EP - 305

JO - Electronic transactions on numerical analysis

JF - Electronic transactions on numerical analysis

ER -

An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

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Keywords

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