A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions
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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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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
Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels
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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
Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel
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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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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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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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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
A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations
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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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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
A new operational approach for solving weakly singular integro-differential equations
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DOI: 10.15672/hjms.2017.519
Abstract: Based on Jacobi polynomials, an operational method is proposed to solve weakly singular integro–differential equations. These equations appear in various fields of science such as physics and engineering, the motion of a plate in a… read more here.
Keywords: integro differential; singular integro; differential equations; approach ... See more keywords