Question

obtain tha radius of convergence of the neumann series when the function f(s) and the kernel k(s,t) are continuous in the interval (a,b)​

Answer 1

Answer:

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Answer 2

Answer:

Radius of convergence of the Neumann series

Step-by-step explanation:

The aim of the method presented in this paragraph is to express the solution of the Helmholtz equation as a series. In practice, only the first term or the first two terms are used. The series is called the Neumann series.

for all x in a domain Γ. K is an integral operator on Γ.

Any kind of diffraction problem described by a Helmholtz equation with constant coefficients can be replaced by an integral problem of this type, by using a Green’s formula for example, ψ could represent the sound field emitted in the presence of an obstacle, ψ0 would be the incident field and Γ the boundary of the obstacle.Many and probably most integral equations cannot be solved by the specialized techniques of the preceding section. Here we develop a rather general technique for solving integral equations. The method, due largely to Neumann, Liouville, and Volterra, develops the unknown function φ(x) as a power series in λ, where λ is a given constant. The method is applicable whenever the series converges.

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