Approximate double series solution to certain Fredholm integral equations of the first kind
نویسندگان
چکیده
منابع مشابه
Convergence Rates of Certain Approximate Solutions to Fredholm Integral Equations of the First Kind*
where S, T are closed, bounded intervals of the real line, K(t, s) is a given kernel on T x S with appropriate properties, and u(t) is known only for t E A = (t1 ) t, )..., t,J, where tl < t2 < *.. < t, , [tl , tn] = T. Letting u(t*) = ui , we take as an approximate solution the function 2 which satisfies Uf = s K(ti , s) S(s) ds, i = 1, 2,..., n (1.2) s and minimizes a quadratic functional J(z...
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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 اولCollocation and Fredholm Integral Equations of the First Kind
We consider the problem of numerical inversion of Fredholm integral equations of the first kind via piecewise interpolation. One of the most important aspects of this technique is the choice of grid and collocation points. Theoretical results are developed which identify an optimal strategy for the distribution of collocation points for piecewise constant interpolation. The method, as outlined,...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1989
ISSN: 0022-247X
DOI: 10.1016/0022-247x(89)90041-3