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   Articles with "weakly singular" as a keyword



A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions

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recommendations! Published in 2021 at "Engineering with Computers"

DOI: 10.1007/s00366-020-00953-9

Abstract: The main purpose of this work is to develop a spectrally accurate collocation method for solving weakly singular integral equations of the second kind with nonsmooth solutions in high dimensions. The proposed spectral collocation method… read more here.

Keywords: method; equations nonsmooth; nonsmooth solutions; integral equations ... See more keywords

A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels

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recommendations! Published in 2019 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-019-00987-2

Abstract: The classical integer-order Jacobi spectral methods for solving second kind nonlinear Volterra integral equations with weakly singular kernels may cause a low-order accuracy in numerically approximating the exact solution. To overcome the shortcomings, we in… read more here.

Keywords: collocation; integral equations; volterra integral; fractional spectral ... See more keywords
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Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels

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recommendations! Published in 2020 at "Numerical Algorithms"

DOI: 10.1007/s11075-020-00877-x

Abstract: In this paper, we consider product integration method based on orthogonal polynomials to solve mixed system of Volterra integral equations of the first and second kind with weakly singular kernels. For investigation of the theoretical… read more here.

Keywords: integration method; product integration; method; weakly singular ... See more keywords
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Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel

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recommendations! Published in 2018 at "International Journal of Applied and Computational Mathematics"

DOI: 10.1007/s40819-018-0580-0

Abstract: In this paper, we consider the Legendre Galerkin and Legendre collocation methods for solving the Fredholm–Hammerstein integral equation with weakly singular kernels. We evaluate the convergence rates for both the methods in both $$L^2$$L2 and… read more here.

Keywords: spectral projection; legendre galerkin; legendre spectral; iterated legendre ... See more keywords

Data-sparse approximation on the computation of a weakly singular Fredholm equation

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recommendations! Published in 2017 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2016.08.010

Abstract: Data-sparse representation techniques are emerging on computing approximate solutions for large scale problems involving matrices with low numerical rank. This representation provides both low memory requirements and cheap computational costs.In this work we consider the… read more here.

Keywords: data sparse; sparse; representation; sparse approximation ... See more keywords

Spectral collocation method for weakly singular Volterra integro-differential equations

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recommendations! Published in 2019 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2019.04.011

Abstract: Abstract Spectral collocation methods are developed for weakly singular Volterra integro-differential equations (VIDEs). Convergence analysis results show that global convergence order depends on the regularities of the kernels functions and solutions to VIDEs, and the… read more here.

Keywords: integro differential; singular volterra; volterra integro; weakly singular ... See more keywords

Error analysis of Jacobi–Galerkin method for solving weakly singular Volterra–Hammerstein integral equations

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recommendations! Published in 2020 at "International Journal of Computer Mathematics"

DOI: 10.1080/00207160.2020.1714601

Abstract: ABSTRACT In this article, Jacobi spectral Galerkin method and its iterated version are developed for second kind weakly singular Volterra–Hammerstein integral equations. We transform the domain of integration from to by using variable and function… read more here.

Keywords: volterra hammerstein; method; hammerstein integral; singular volterra ... See more keywords

Gauss quadrature rules for integrals involving weight functions with variable exponents and an application to weakly singular Volterra integral equations

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recommendations! Published in 2025 at "IMA Journal of Numerical Analysis"

DOI: 10.1093/imanum/drae088

Abstract: This paper presents a numerical integration approach that can be used to approximate on a finite interval, the integrals of functions that contain Jacobi weights with variable exponents. A modification of the integrand close to… read more here.

Keywords: variable exponents; integral equations; weakly singular; volterra integral ... See more keywords

A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations

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recommendations! Published in 2017 at "International Journal of Computational Methods"

DOI: 10.1142/s0219876217500220

Abstract: In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli… read more here.

Keywords: nonlinear weakly; wavelet method; method; bernoulli wavelet ... See more keywords

Fractional integration operator for numerical solution of the integro-partial time fractional diffusion heat equation with weakly singular kernel

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recommendations! Published in 2017 at "Asian-european Journal of Mathematics"

DOI: 10.1142/s1793557117500711

Abstract: In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference approximation followed by applying the… read more here.

Keywords: singular kernel; time fractional; time; solution ... See more keywords

Weighted Weakly Singular Integral Inequalities: New Explicit Bounds and Applications in Fractional Dfferential Equations

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recommendations! Published in 2025 at "Journal of Mathematics"

DOI: 10.1155/jom/8311840

Abstract: This study delves into the formulation of innovative integral inequalities, specifically designed to accommodate weakly singular singularities, thus significantly broadening the scope of previously established ones. The methodology employed centers around the application of weighted… read more here.

Keywords: weighted weakly; weakly singular; integral inequalities; applications fractional ... See more keywords