Results 31 to 40 of about 576 (215)
Axioms, 2022 This article investigates an equation with a rapidly oscillating inhomogeneity and with a rapidly decreasing kernel of an integral operator of Fredholm type.
Dana Bibulova +2 more
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On the Volterra integral equation with weakly singular kernel [PDF]
Mathematica Bohemica, 2006 Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.
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International Journal of Differential Equations, 2018 An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM).
Rezvan Ghoochani-Shirvan +2 more
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Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation
Journal of Mathematics, 2022 This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix.
Ioannis Dassios +2 more
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Fractal and Fractional, 2023 We offer a wavelet collocation method for solving the weakly singular integro-differential equations with fractional derivatives (WSIDE). Our approach is based on the reduction of the desired equation to the corresponding Volterra integral equation.
Haifa Bin Jebreen
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Fredholm and Volterra integral equations with integrable singularities
Hokkaido Mathematical Journal, 2004 The authors present a number of results on the existence of continuous nonnegative solutions \(y\) of the Fredholm equation \[ y(t) = \int_J k(t,s) f(s,y(s))\,ds, \quad t \in J, \tag{F} \] where either \(J = [0,1]\) or \(J = [0,\infty)\), and for the Volterra equation \[ y(t) = \int_0^t k(t,s) f(s,y(s))\,ds, \quad t \in [0,T].
AGARWAL, Ravi P., O'REGAN, Donal
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Solutions of Nonlinear Integral Equations and their Application to Singular Perturbation Problems [PDF]
, 1963 [See thesis for full ...
Willett, Douglas Warren
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Approximation Solution of Fuzzy Singular Volterra Integral Equation by Non-Polynomial Spline
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In
Zahraa A. Ibrahim, Nabaa N. Hasan
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Collocation Solutions of a Weakly Singular Volterra Integral Equation
Trends in Computational and Applied Mathematics, 2007 The discrete superconvergence properties of spline collocation solutions for a certain Volterra integral equation with weakly singular kernel are analyzed.
T. Diogo, P. Lima
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Boundary Value Problems, 2018 We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary condition, with a real parameter ...
Mahdi Boukrouche, Domingo A. Tarzia
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