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Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side

Jacek Gulgowski (2014)

Open Mathematics

We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea of replacing a measurable function in the right-hand side of the problem with its Kantorovich polynomial. We will show that this approximation scheme recovers essential solutions to the original BVP. We also consider the corresponding finite dimensional problem. We suggest a suitable mapping of solutions to finite dimensional problems to piecewise constant...

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