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

• Autorzy: Jacek Gulgowski
• Języki publikacji: EN

Abstrakty

EN

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 functions so that the later approximate a solution to the original BVP. That is why the presented idea may be used in numerical computations.

Słowa kluczowe

EN

Picard problem; Kantorovich polynomial; Approximation of BVP solution

Kategorie tematyczne

• 34A45: Theoretical approximation of solutions
• 65L10: Boundary value problems
• 34B24: Sturm-Liouville theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 1
• Strony: 155-166

Daty

wydano

2014-01-01

online

2013-10-30

Twórcy

autor

Jacek Gulgowski

• University of Gdańsk

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0323-8