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   Articles with "volterra integral" as a keyword



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Analysis of collocation methods for nonlinear Volterra integral equations of the third kind

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recommendations! Published in 2019 at "Calcolo"

DOI: 10.1007/s10092-019-0304-9

Abstract: We study the approximation of solutions of a class of nonlinear Volterra integral equations (VIEs) of the third kind by using collocation in certain piecewise polynomial spaces. If the underlying Volterra integral operator is not… read more here.

Keywords: integral equations; volterra integral; third kind; collocation ... See more keywords
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Itô Differential Representation of Singular Stochastic Volterra Integral Equations

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recommendations! Published in 2020 at "Acta Mathematica Scientia"

DOI: 10.1007/s10473-020-0624-5

Abstract: In this paper we obtain an Itô differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for… read more here.

Keywords: stochastic volterra; differential representation; integral equations; singular stochastic ... See more keywords
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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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Legendre–Galerkin Methods for Third Kind VIEs and CVIEs

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recommendations! Published in 2020 at "Journal of Scientific Computing"

DOI: 10.1007/s10915-020-01187-z

Abstract: The main purpose of this paper is to present a spectral Legendre–Galerkin method for solving Volterra integral equations of the third kind. When the operator associated with the equivalent Volterra integral equations of second kind… read more here.

Keywords: kind; legendre galerkin; method; third kind ... See more keywords
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Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Convolution Itô-Volterra Integral Equations with Constant Delay

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recommendations! Published in 2019 at "Methodology and Computing in Applied Probability"

DOI: 10.1007/s11009-019-09702-y

Abstract: This paper mainly focuses on the strong convergence of the Euler-Maruyama method for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay. It is well known that the strong approximation of the Itô integral usually… read more here.

Keywords: integral equations; equations constant; volterra integral; stochastic convolution ... See more keywords
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A new contraction condition and its application to weakly singular Volterra integral equations of the second kind

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recommendations! Published in 2017 at "Journal of Fixed Point Theory and Applications"

DOI: 10.1007/s11784-017-0445-x

Abstract: In this paper, we prove some results concerning the existence and uniqueness of solutions for a large class of nonlinear Volterra integral equations of the second kind, especially singular Volterra integral equations, in the Banach… read more here.

Keywords: second kind; new contraction; equations second; volterra integral ... See more keywords
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Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

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recommendations! Published in 2018 at "Computational and Applied Mathematics"

DOI: 10.1007/s40314-017-0563-5

Abstract: In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods… read more here.

Keywords: order; spectral projection; order mathcal; legendre spectral ... See more keywords
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A spectral iterative method for solving nonlinear singular Volterra integral equations of Abel type

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recommendations! Published in 2017 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2016.09.008

Abstract: Abstract In this paper, a spectral iterative method is employed to obtain approximate solutions of singular nonlinear Volterra integral equations, called Abel type of Volterra integral equations. The Abel's type nonlinear Volterra integral equations are… read more here.

Keywords: spectral iterative; iterative method; abel type; integral equations ... See more keywords
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Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities

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recommendations! Published in 2020 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2019.12.013

Abstract: Abstract Filon collocation methods are well known for their good performances in solving the second-kind highly oscillatory Volterra integral equations with weak singularities. As the frequency increases, these methods can provide much more accurate solutions… read more here.

Keywords: frequency; highly oscillatory; collocation methods; volterra integral ... See more keywords
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A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

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recommendations! Published in 2017 at "Applicable Analysis"

DOI: 10.1080/00036811.2016.1208815

Abstract: In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of… read more here.

Keywords: integral equations; nonlinear stratonovich; solving nonlinear; volterra integral ... See more keywords
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Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels

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recommendations! Published in 2023 at "International Journal of Computer Mathematics"

DOI: 10.1080/00207160.2023.2203786

Abstract: In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly… read more here.

Keywords: highly oscillatory; collocation methods; interpolation collocation; collocation ... See more keywords