منابع مشابه
Integral 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 کاملCARMA processes as solutions of integral equations
A CARMA(p, q) process is defined by suitable interpretation of the formal p order differential equation a(D)Yt = b(D)DLt, where L is a two-sided Lévy process, a(z) and b(z) are polynomials of degrees p and q, respectively, with p > q, and D denotes the differentiation operator. Since derivatives of Lévy processes do not exist in the usual sense, the rigorous definition of a CARMA process is bas...
متن کاملPhase functions as solutions of integral equations
A phase function is an important characteristic of a scattering medium. A method to derive new analytic phase functions is proposed. The relation between a phase function and an angle-averaged single-scattering intensity, derived earlier [M. L. Shendeleva, J. Opt. Soc. Am. A 30, 2169 (2013)], is considered as an integral equation for a phase function. This equation is classified as an Abel inte...
متن کاملApproximate solution of dual integral equations
We study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polynomials, we propose a method to approximate the solution of Cauchy type singular integral equation which will ...
متن کاملSPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1982
ISSN: 0022-0396
DOI: 10.1016/0022-0396(82)90054-7