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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
Mathematics, 2022 A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems.
Ilya Boykov +2 more
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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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SINGULAR INTEGRAL EQUATIONS AND APPLICATIONS TO NONLINEAR CONJUGATE PROBLEMS [PDF]
Taiwanese Journal of Mathematics, 2010 In this paper, we establish the existence of multiple positive solutions for singular integral equations. The proof is based on a general existence principle established using a nonlinear alternative principle of Leray-Schauder type and a well-known fixed point theorem in cones.
Chu, Jifeng, O'Regan, Donal
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Fractal and Fractional, 2023 The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim +3 more
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Singularity Subtraction for Nonlinear Weakly Singular Integral Equations of the Second Kind [PDF]
, 2019 The singularity subtraction technique for computing an approximate solution of a linear weakly singular Fredholm integral equation of the second kind is generalized to the case of a nonlinear integral equation of the same kind. Convergence of the sequence of approximate solutions to the exact one is proved under mild standard hypotheses on the ...
Ahues, Mario +3 more
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Some weakly singular Volterra integral inequalities with maxima in two variables
Journal of Inequalities and Applications, 2023 In this paper, we establish some new weakly singular Volterra type integral inequalities that include the maxima of the unknown function of two variables.
Yining Sun, Run Xu
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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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Advances in Difference Equations, 2018 This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind.
Bijan Hasani Lichae +2 more
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Monotonic solutions of functional integral and differential equations of fractional order
Electronic Journal of Qualitative Theory of Differential Equations, 2009 The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations.
Ahmed El-Sayed, H. H. G. Hashem
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Two Singularity Subtraction Schemes for a Class of Nonlinear Weakly Singular Integral Equations
Numerical Functional Analysis and Optimization, 2022 Singularity subtraction for linear weakly singular Fredholm integral equations of the second kind is generalized to nonlinear integral equations. Two approaches are presented: The Classical Ap proach discretizes the nonlinear problem, and uses some finite dimensional linearization process to solve numerically the discrete problem.
Ahues, M. +3 more
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