Rainer Kress. Linear Itegral Equatios. Springer-Verlag, New York, 1989.  Home/Search   Document Not in Database   Summary   Related Articles

....obtained by summing the iterated kernels of 11 orders up to m( z) k( z) 44) where k0 is taken to be the identity. Finally, we can express the tth approximation f, in terms of the kernel m: f, f m ( g(y) ds. 45) 5. 2 Successive Approximations The method of successive appcoximatiots [5, 22] is a slight variation on the Neumann series. Rather than focusing on the operators or their kernels, as in the previous section, we formulate an iterative scheme based on the functions. Using the previous definitions, we h f, Mg = g Kg K2g . Kg. 46) It follows immediately that the ....

....the corresponding integral equation, we have the simple recurrence relation: f (x) g(x) x, y) f(y) Because equation (41) holds for f, we are guaranteed that f converges to f as n whenever I IKll 1. 5. 3 The NystrSm Method The Nystr Bm method, also known as the quadrature method [22, 9], is one of the most straightforward numerical methods for integral equations It directly exploits the similarity between the kernel of an integral operator and its finite dimensional analog, the matrix. The idea is to estimate the action of the integral operator by a quadrature rule, producing a ....

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Rainer Kress. Linear Itegral Equatios. Springer-Verlag, New York, 1989.

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