Results 21 to 30 of about 7,526 (199)
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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Semi-spectral Chebyshev method in Quantum Mechanics [PDF]
, 2006 Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics ...
A. Deloff +34 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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Ulam–Hyers stabilities of a differential equation and a weakly singular Volterra integral equation
Journal of Inequalities and Applications, 2021 In this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on the Banach fixed point theorem in some space of continuous functions equipped with the norm ∥ ⋅ ∥ ∞ $\|\cdot \|_{\infty }$ . Moreover, we get some results on
Ozgur Ege, Souad Ayadi, Choonkil Park
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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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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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High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels [PDF]
, 1974 The solution of the Volterra integral equation, \[ ( * )\qquad x(t) = g_1 (t) + \sqrt {t}g_2 (t) + \int _0^t \frac {K(t,s,x(s))} {\sqrt {t - s} } ds, \quad 0 \leqq t \leqq T,\] where $g_1 (t)$, $g_2 (t)$ and $K(t,s,x)$ are smooth functions, can be ...
de Hoog, Frank, Weiss, Richard
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Asymptotic Solutions of Linear Volterra Integral Equations With Singular Kernels [PDF]
Transactions of the American Mathematical Society, 1974 Volterra integral equations of the form u ′ ( t ) = − ∫ 0 t a ( t − τ ) u ( τ ) d τ , u ( 0 ) = 1 u’(t) = - \smallint _0^ta(
Wong, J. S. W., Wong, R.
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