Abstract
We give an elementary proof of the existence and uniqueness of solution of Bessel's nonlinear differential equation by using a sequence of approximations {un (x)} which are the exact solutions of a linearized form of the original equation. We show that {un (x)} converges uniformly to the solution of Bessel's equation, and that the rate of convergence as n approaches ∞ is quadratic. The integration of the solution on the different intervals of definition is a non-well posed problem. In the numerical integration of the solution, we have associated the Tau method to the regularization of order zero of Tikhonov.
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