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

Jacek Gulgowski

Open Mathematics (2014)

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

Abstract

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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.

How to cite

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Jacek 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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