Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method

Babayar-Razlighi, Bahman; Soltanalizadeh, Babak

doi:10.1016/j.mcm.2013.06.016

Cited by 11 publications

(3 citation statements)

References 14 publications

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“…{r1 -> 2 h})} . {a1, a2, a3, b1, b2}) // Simplify; {b, A} = Simplify@ CoefficientArrays[{eq1, eq2, eq3, eq4, eq5}, {a1, a2, a3, b1, b2}]; sol = Simplify@(Inverse b1 -> sol2[ [4]], b2 -> sol2[ [5]]}, {h, 0, 4}] // FullSimplify)…”

Section: Fundingmentioning

confidence: 99%

“…Compared to other interpolation methods, RBFs provide more accurate approximations in high-dimensional spaces [2]. RBFs [3] (Chapter 3) have received interest from researchers in both engineering [4,5] and scientific domains [6,7]. They can also be employed for function approximation problems, where the target is to find a function that models the input-output relationship of a given system.…”

Section: Introduction 1goalsmentioning

confidence: 99%

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Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Liu,

Shateyi

2024

Mathematics

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An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems.

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Section: Fundingmentioning

confidence: 99%

Section: Introduction 1goalsmentioning

confidence: 99%

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Liu,

Shateyi

2024

Mathematics

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show abstract

“…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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Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Arqub

2015

Neural Comput & Applic

343

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Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method

Cited by 11 publications

References 14 publications

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

RBFs for Integral Equations with a Weakly Singular Kernel

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

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