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An Algorithm for the Solution of Nonlinear Volterra–Fredholm Integral Equations with a Singular Kernel

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
M A Abdel-Aty, Mohamed E Nasr, Abdou Mohamed A   +2 more
exaly   +3 more sources

A Singular Nonlinear Volterra Integral Equation

Journal of Integral Equations and Applications, 1993
Many problems in Applied Mathematics lead to the study of the nonlinear partial differential equation \(u_ t = (a(u))_{xx} + (b(u))_ x + c(u)\). The interest in the existence of travelling-wave solutions of the form \(U(x,t) = U(\psi)\), \(\psi = x - \lambda t\), originates an ordinary differential equation from which arise integral equations of the ...
exaly   +5 more sources

Existence of solutions for a class of nonlinear Volterra singular integral equations

Computers and Mathematics With Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Józef Banas, Yaghoub Jalilian, Asadollah Aghajani   +2 more
exaly   +3 more sources

Research on Chaos of Nonlinear Singular Integral Equation

Journal of Applied Mathematics and Physics, 2023
Yannan Liu, Yu Wang
exaly   +2 more sources

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
doaj   +1 more source

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, Aman Ullah, Kamal Shah, Dumitru Baleanu   +3 more
doaj   +1 more source

Continuous operator method application for direct and inverse scattering problems

Журнал Средневолжского математического общества, 2021
We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems.
Boykov Ilya V., Roudnev Vladimir A., Boykova Alla I., Stepanov Nikita S.   +3 more
doaj   +1 more source

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
openaire   +2 more sources

The Müntz–Legendre Wavelet Collocation Method for Solving Weakly Singular Integro-Differential Equations with Fractional Derivatives

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
doaj   +1 more source

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, Vladimir Roudnev, Alla Boykova   +2 more
doaj   +1 more source