Nonlinear integral equations singular in the dependent variable
Applied Mathematics Letters, 2007 This paper concerns the existence of nonnegative solutions to the singular integral equation \(y(t)=\int^1_0 k(t,s)[G(s,y(s))+F(s,y(s))]ds\) \((t\in [0,1])\), where \(G\in C([0,1]\times (0,\infty),[0,\infty))\), \(F\in C([0,1]\times [0,\infty),[0,\infty))\) so \(G\) may be singular at \(y=0\).
O’Regan, Donal +2 more
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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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Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow [PDF]
, 1972 The problem considered here is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum.
Whitney, Arthur K.
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The Sivashinsky equation for corrugated flames in the large-wrinkle limit [PDF]
, 2008 Sivashinsky's (1977) nonlinear integro-differential equation for the shape of corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem, involving the 2N complex poles of the flame slope.
Bruno Denet +13 more
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Numerical treatments for solving nonlinear mixed integral equation
Alexandria Engineering Journal, 2016 We consider a mixed type of nonlinear integral equation (MNLIE) of the second kind in the space C[0,T]×L2(Ω ...
M.A. Abdou, M. Basseem
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Robust and efficient solution of the drum problem via Nystrom approximation of the Fredholm determinant [PDF]
, 2014 The drum problem-finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition-has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed.
Barnett, Alex, Zhao, Lin
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Boundary Value Problems, 2022 We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 $t=0$ , 1.
Debao Yan
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Singular integral inequalities with several nonlinearities and integral equations with singular kernels [PDF]
Nonlinear Oscillations, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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. +3 more
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Slow invariant manifolds as curvature of the flow of dynamical systems [PDF]
, 2014 Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e.
Chua, Leon +2 more
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