Results 261 to 270 of about 1,686 (292)

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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A Collocation Method for Weakly Singular Fredholm Integral Equation

2015 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, 2015
A collocation method is introduced for a class of Fred Holm integral equation of the second kind with weakly singular kernels. The key idea of this method is splitting the weakly singular kernel of the integral operator into finite parts so that the weak singularity is concentrated in one which can be analytically solved using integration by parts ...
Xiao-Ya Lv, Wei-Hua Luo
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Numerical solutions of weakly singular Hammerstein integral equations

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chafik Allouch, Driss Sbibih, Mohamed Tahrichi   +2 more
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On Weakly Singular Integral Equations of the Second Kind

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1988
The note is concerned with the numerical solution of Fredholm integral equations \[ \lambda x(t)-\int^{b}_{a}k(t,s)g_{\alpha}(| t- s|)x(s)ds=f(t), \] where f and k are given and smooth and \(g_{\alpha}(r)=r^{\alpha -1 ...
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Quadrature methods for periodic singular and weakly singular Fredholm integral equations

Journal of Scientific Computing, 1988
High-accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations (Romberg-type integration formulas).
Avram Sidi, Moshe Israeli
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Solution of a class of Volterra integral equations with singular and weakly singular kernels

Applied Mathematics and Computation, 2008
The purpose of the paper is to derive the solution to a Volterra integral equation \[ y(t)=g(t)+\int^t_0\frac{s^{\mu-\nu}}{t^\mu}y(s)\,ds\quad ...
Bao-Qing Tang, Xian-Fang Li
openaire   +1 more source

A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels [PDF]

SIAM Journal on Numerical Analysis, 2003
The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent ...
Yanzhao Cao
exaly   +2 more sources

Information complexity of weakly singular integral equations

Ukrainian Mathematical Journal, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pereverzev, S. V., Makhkamov, K. Sh.
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What is the complexity of weakly singular integral equations?

AIP Conference Proceedings, 2012
We discuss bounds of fast solving weakly singular Fredholm integral equations when the information about the smooth coefficient functions in the kernel and about the free term is restricted to a given number of sample values. In this situation, a fast/quasifast solver is constructed.
Arvet Pedas, Gennadi Vainikko
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Product Integration for Weakly Singular Integral Equations In ℝm

1985
In this note we discuss the numerical solution of the second kind Fredholm integral equation: $$ y(t) = f(t) + \lambda \int\limits_{\Omega } {{{\psi }_{\alpha }}(|t - s|)g(t,s)y(s)ds,\;t \in \bar{\Omega },} $$ (1) Where \( \lambda \in ;\not{ \subset }\backslash \{ 0\} \) , the functions f,g are given and continuous, |.| denotes the Euclidean ...
Ivan G. Graham, Claus Schneider
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