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

Open Mathematics (2014)

- Volume: 12, Issue: 1, page 155-166
- ISSN: 2391-5455

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topJacek Gulgowski. "Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side." Open Mathematics 12.1 (2014): 155-166. <http://eudml.org/doc/269347>.

@article{JacekGulgowski2014,

abstract = {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.},

author = {Jacek Gulgowski},

journal = {Open Mathematics},

keywords = {Picard problem; Kantorovich polynomial; Approximation of BVP solution; Kantorovich polynomial approximation; approximation of BVP solution},

language = {eng},

number = {1},

pages = {155-166},

title = {Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side},

url = {http://eudml.org/doc/269347},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Jacek Gulgowski

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

JO - Open Mathematics

PY - 2014

VL - 12

IS - 1

SP - 155

EP - 166

AB - 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.

LA - eng

KW - Picard problem; Kantorovich polynomial; Approximation of BVP solution; Kantorovich polynomial approximation; approximation of BVP solution

UR - http://eudml.org/doc/269347

ER -

## References

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