The semi-explicit Volterra integral algebraic equations with weakly singular kernels: The numerical treatments

Pishbin, S.; Ghoreishi, F.; Hadizadeh, M.

doi:10.1016/j.cam.2012.12.012

Cited by 33 publications

(4 citation statements)

References 14 publications

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“…The FIDAEs are a generalization of integral and integrodifferential equations with algebraic constraints which arise in the problem of evaluation of a chemical reaction within a small cell [30], dynamic processes in chemical reactors [31], identification of memory kernels in heat conduction and viscoelasticity [32] and etc. [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

Talib¹,

Mohammed²

2022

ANJS

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In this paper, we will use an artificial neural network (ANN) to solve the variable order fractional integro-differential algebraic equations (VFIDAEs), which is a three-layer feed-forward neural architecture that is formed and trained using a back propagation unsupervised learning algorithm based on the gradient descent rule for minimizing the error function and parameter modification (weights and biases).When we combine the initial conditions with the ANN output, we get a good approximation of the VFIDAE solution. Finally, the analysis is complemented by two numerical examples that demonstrate the method capability. The collected results show that the suggested strategy is quite successful, resulting in superior approximations in these cases.

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Section: Introductionmentioning

confidence: 99%

Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

Talib¹,

Mohammed²

2022

ANJS

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“…It is difficult to solve these equations analytically, hence numerical solutions are required. Singular integral equations have been approached by different methods including Collocation method [2][3][4], Reproducing kernel method [17], Galerkin method [5], Adomian decomposition method [1], Homotopy perturbation method [6], Radial Basis Functions [10,11], Newton product integration method [7], and many others.…”

Section: Introductionmentioning

confidence: 99%

RBFs for Integral Equations with a Weakly Singular Kernel

Biazar

Asadi²

2015

AJAM

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In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.

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“…It is well known that there are many numerical methods for solving second kind Volterra integral equations such as the Runge-Kutta method and the collocation method based on piecewise polynomials; see, for example, Brunner [1] and references therein. For more information of the progress on the study of the problem, we refer the readers to [2][3][4][5][6][7][8]. Recently, a few works touched the spectral approximation to Volterra integral equations.…”

Section: Introductionmentioning

confidence: 99%

A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

Guo

Cai

Xin

2014

Abstract and Applied Analysis

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The purpose of this paper is to provide a Jacobi-collocation method for solving second kind Volterra integral equations with a smooth kernel. This method leads to a fully discrete integral operator. First, it is shown that the fully discrete integral operator is stable in bothL∞and weightedL2norms. Then, the proposed approach is proved to arrive at an optimal (the most possible) convergent order in both norms. One numerical example demonstrates the efficiency and accuracy of the proposed method.

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The semi-explicit Volterra integral algebraic equations with weakly singular kernels: The numerical treatments

Cited by 33 publications

References 14 publications

Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

RBFs for Integral Equations with a Weakly Singular Kernel

A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

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