منابع مشابه
On Laplace ' S Integral Equations
which is known in the literature as Laplace's integral equation. The contour (C) and the function f(z) are supposed given and F(x) is to be found. In the case when the contour (C) consists of the positive part of the axis of reals, the solution of the equation (*■) was given by H. Poincaré t and H. Hamburger. % Each of these authors considers F(x) as a function of the real variable *. When the ...
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In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملIntegral Equations
We show how Mathematica can be used to obtain numerical solutions of integral equations by exploiting a combination of iteration and interpolation. The efficacy of the method is demonstrated by considering three classical integral equations of applied mathematics: Love’s equation for the condenser problem, Theodorsen’s equation associated with conformal mapping, and Nekrasov’s equation arising ...
متن کاملAdvanced School on Integral Equations and Applications
Integral equations are an important subject within applied mathematics. They are used as mathematical models for many and varied physical situations, and also occur as reformulations of other mathematical problems. The aim of this course is to provide basic notions for a complete knowledge of the classical and advanced methods for the numerical solution of integral equations.
متن کاملOn Monotonic Solutions of Some Integral Equations
Integral equations arise naturally in applications of real world problems [5, 6, 7, 8]. The theory of integral equations has been well developed with the help of various tools from functional analysis, topology and fixed-point theory. The classical theory of integral equations can be generalized if one uses the Stieltjes integral with kernels dependent on one or two variables. The aim of this p...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1926
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1926-1501354-4