Singular nonlinear integral equations

Applied Mathematics and Computation, 2004
Assuming that \(L\) is a sufficiently well behaved closed contour in the complex plane, the authors investigate the nonlinear Cauchy singular integral equation \[ \phi(t) = \Omega \sum_{j=0}^{m-1} a_j(t) \int_L { G(\alpha_j(t), \tau, \phi(\tau)) \over \tau - \alpha_j(t)} d \tau\text{ for }t \in L. \] Here \(\alpha_0(t) = t\) and \(\alpha_j(t) = \alpha(\
S. M. Amer, S. Dardery
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Matrix Method by Genocchi Polynomials for Solving Nonlinear Volterra Integral Equations with Weakly Singular Kernels

Symmetry, 2020
In this study, we present a spectral method for solving nonlinear Volterra integral equations with weakly singular kernels based on the Genocchi polynomials.
Elham Hashemizadeh, Samad Noeiaghdam, Noeiaghdam Samad +2 more
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Singular nonlinear integral equations of Hammerstein type

Lecture Notes in Mathematics, 1975
Felix E Browder, Browder Felix E
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On the Solvability of Nonlinear Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1993
Three classes of nonlinear singular integral equations of Cauchy type occuring in the treatment of certain free boundary value problems are investigated. Existence of the solution is proved under weaker conditions than in [13] using the technique which was created in [12, 13] and is based on the application of Schauder’s fixed point theorem.
Junghanns, P., Weber, U.
openaire +1 more source

mathematics
numerical methods for integral equations
existence

fixed point theorem
nonlinear singular integral equation
collocation method

singular integral equations
convergence
volterra integral equations