Complexity, 2019 In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays.
Li Zhang +3 more
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A Nyström interpolant for some weakly singular nonlinear Volterra integral equations
Journal of Computational and Applied Mathematics, 2009 The author considers the numerical solution of second kind Volterra integral equations with weakly singular kernel which is a non-compact operator, of the type \[ u(t)- \int^t_0 k(t,s)\Biggl({s\over t}\Biggr)^\mu {u(s)\over s} ds= f(t),\qquad t\in (0,T]> 0,\;\mu> 0, \] and \(f(t)\) a given function.
Baratella, Paola
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Computation of semi-analytical solutions of fuzzy nonlinear integral equations
Advances in Difference Equations, 2020 In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A
Zia Ullah +3 more
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A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems
Fractal and Fractional, 2023 Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs).
Mohammadhossein Derakhshan +4 more
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Volterra integral equations: the singular case
Hokkaido Mathematical Journal, 2003 The authors are concerned with the investigation of singular Volterra integral equations of the form \[ y(t)= \int^t_0 k(t, s) f(s,y(s))\,ds,\quad t\in [0,T]. \] The singularity feature appears in the nonlinearity \(f(t,y)\), which may admit a nonregular behavior at \(y= 0\).
AGARWAL, Ravi P., O'REGAN, Donal
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Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique [PDF]
Computational Algorithms and Numerical DimensionsThis study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented.
Youssef Esmaiel +2 more
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Singular Integral Equations of the Volterra Type [PDF]
Transactions of the American Mathematical Society, 1914 Equations of the form (1) sometimes arise,1: however, for which the conditions of Evans's theorem are not satisfied. Various cases in which this is true are considered in the present paper. In each instance an attempt is made not merely to prove the existence of a continuous solution, but also to determine its behavior for large values of x.
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Comparative analysis of the influence of creep of concrete composite beams of steel - concrete model based on Volterra integral equation [PDF]
Građevinski Materijali i Konstrukcije, 2017 The paper presents analysis of the stress-strain behaviour and deflection changes due to creep in statically determinate composite steel-concrete beam according to EUROCODE 2, ACI209R-92 and Gardner&Lockman models.
Partov Doncho, Kantchev Vesselin
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Efficient solution of a wave equation with fractional-order dissipative terms [PDF]
, 2009 We consider a wave equation with fractional-order dissipative terms modeling viscothermal losses on the lateral walls of a duct, namely the Webster-Lokshin model.
Haddar, Houssem +6 more
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On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations
Mathematics, 2022 An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs).
Haifa Bin Jebreen, Ioannis Dassios
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