Results 1 to 10 of about 3,392 (297)

A numerical approach to fractional Volterra-Fredholm integro-differential problems using shifted Chebyshev spectral collocation. [PDF]

Sci Rep
Hamood MM, Sharif AA, Ghadle KP.
europepmc   +1 more source

The method of Kantorovich majorants to nonlinear singular integral equation with shift

Applied Mathematics and Computation, 2009
For a simple closed contour \(L\) in the complex plane and a shift function \(\alpha\) satisfying \(\alpha(\alpha(t))=t\) the nonlinear singular integral equation \[ \begin{multlined} a(t)u(t)+b(t)u(\alpha(t))+ {c(t)\over\pi i}\int_L{u(\tau)\over\tau-t}\,d\tau + {d(t)\over\pi i}\int_L{u(\tau)\over\tau-\alpha(t)}\,d\tau\\ - {1\over\pi i}\int_L\Bigl ...
S. M. Amer, S. Dardery
exaly   +2 more sources

ON THE METHOD OF SOLUTION FOR A KIND OF NONLINEAR SINGULAR INTEGRAL EQUATION

Acta Mathematica Scientia, 2004
The author considers the nonlinear singular integral equation \[ \phi(t)^{2}+\frac{2b}{\pi i}\int_{L}\frac{\phi(\tau)}{\tau-t}d\tau=f(t), \quad t\in L, \] where \(L\) is a closed countour in the complex plane, \(b\not=0\) is a constant and \(f(t)\) is a polynomial. Certain special cases of the above equation are considered.
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Newton–Kantorovich approximations to nonlinear singular integral equation with shift

Applied Mathematics and Computation, 2011
The paper is concerned with the applicability of some new conditions for the convergence of Newton-Kantorovich approximations to solution of nonlinear singular integral equations of Uryson type with shift. The results are illustrated in generalized Holder space.
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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.
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The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1994
The differential properties of a solution of a nonlinear multidimensional weakly singular integral equation of the Uryson type on an open bounded set G \in \mathbb R^n are examined.
Pedas, A., Vainikko, G.
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Integrability and singularity structure of coupled nonlinear Schrödinger equations

Chaos, Solitons & Fractals, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radhakrishnan, R., Sahadevan, R., Lakshmanan, M.   +2 more
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On a Class of Nonlinear Singular Integral Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1985
The present communication is a continuation of a previous paper by the author [ibid. 63, 249-259 (1983; Zbl 0525.45004)]. In that paper, the author has applied methods of monotone operator theory to some classes of nonlinear singular integral and integro-differential equations of Cauchy type.
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Nonlinear singular integral equations in lebesgue spaces

Journal of Mathematical Sciences, 2011
Using the theory of monotone operators, existence and uniqueness for singular integral equations of the type \[ \lambda_1a(x)u(x)+{\lambda_2\over\pi}\int_a^b {\bigl(w(x)+w(s)\bigr){\mathcal K}(x,s)u(s)\over s-x}ds+ \lambda_3F\bigl(x,u(x)\bigr)=f(x), \] of singular Hammerstein integral equations of the type \[ u(x)+{\lambda\over\pi}\int_a^b {\bigl(w(x ...
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Non‐linear singular integral equations on a finite interval

Mathematical Methods in the Applied Sciences, 2001
AbstractA class of nonlinear singular integral equations of Cauchy type on a finite interval is transformed to an equivalent class of (discontinuous) boundary value problems for holomorphic functions in the complex unit disk. Using recent results on the solvability of explicit Riemann–Hilbert problems, we prove the existence of solutions to the ...
Junghanns, P., Semmler, G., Weber, U., Wegert, E.   +3 more
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