Solution of a class of singular integral equations
نویسندگان
چکیده
منابع مشابه
Numerical solution for a class of singular integral equations
This paper is concerned with finding approximate solution for the singular integral equations. Relating the singular integrals to Cauchy principal-value integrals, we expand the kernel and the density function of singular integral equation by the sum of the chebyshev polynomials of the first, second, third and fourth kinds. Some numerical examples are presented to illustrate the accuracy and ef...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولApproximate solution of singular integral equations
K e y w o r d s I n t e g r a l equations, Cauchy type, Singular kernels. 1. I N T R O D U C T I O N Singular integral equations of the first kind, with a Cauchy type singular kernel, over a finite interval can be represented by the general equation f f _ l f(t)[ko(t,x)+k(t,x)]dt = g(x), 1 < x < 1, (1.1) 1 where ko(t, x) x) t) 0) (1.2) t x ' and k are regular square in tegrab le funct ions of t...
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In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficien...
متن کاملAn effective method for approximating the solution of singular integral equations with Cauchy kernel type
In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1967
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/215029