Jacobi spectral collocation technique for fractional inverse parabolic problem

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

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A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

Abstract and Applied Analysis ◽

10.1155/2018/3569139 ◽

2018 ◽

Vol 2018 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Mohammad Hossein Daliri Birjandi ◽

Jafar Saberi-Nadjafi ◽

Asghar Ghorbani

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Exact Solutions ◽

Iteration Method ◽

Spectral Collocation ◽

Numerical Examples ◽

Integro Differential Equation ◽

Collocation Technique ◽

Computational Work ◽

Novel Method

An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.

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Generic well-posedness of a linear inverse parabolic problem with diffusion parameters

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip.1999.7.3.241 ◽

1999 ◽

Vol 7 (3) ◽

Cited By ~ 16

Author(s):

M. CHOULLI ◽

M. YAMAMOTO

Keyword(s):

Parabolic Problem ◽

Well Posedness ◽

Diffusion Parameters ◽

Inverse Parabolic Problem

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Numerical solution of a semi-linear inverse parabolic problem via HPM

International Journal of Computing Science and Mathematics ◽

10.1504/ijcsm.2016.10000255 ◽

2016 ◽

Vol 7 (4) ◽

pp. 330

Author(s):

Alimardan Shahrezaee ◽

Malihe Rostamian

Keyword(s):

Numerical Solution ◽

Parabolic Problem ◽

Inverse Parabolic Problem

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Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0144 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Mohamed A. Abdelkawy

Keyword(s):

Brownian Motion ◽

Error Analysis ◽

Integral Equations ◽

Lagrange Interpolation ◽

Fredholm Integral Equations ◽

Algebraic Equations ◽

Spectral Collocation ◽

Numerical Examples ◽

Collocation Technique

Abstract This paper addresses a spectral collocation technique to treat the stochastic Volterra–Fredholm integral equations (SVF-IEs). The shifted Legendre–Gauss–Radau collocation (SL-GR-C) method is developed for approximating the FSV-IDEs. The principal target in our technique is to transform the SVF-IEs to a system of algebraic equations. For computational purposes, the Brownian motion W(x) is discretized by Lagrange interpolation. While the integral terms are interpolated by Legendre–Gauss–Lobatto quadrature. Some numerical examples are given to test the accuracy and applicability of our technique. Also, an error analysis is introduced for the proposed method.

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