Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
155-166
Opis fizyczny
Daty
wydano
2014-01-01
online
2013-10-30
Twórcy
autor
- University of Gdańsk, dzak@mat.ug.edu.pl
Bibliografia
- [1] Besov K.O., On the continuity of the generalized Nemytskii operator on spaces of differentiable functions, Math. Notes, 2002, 71(1–2), 154–165 http://dx.doi.org/10.1023/A:1013998928829
- [2] Capietto A., Mawhin J., Zanolin F., On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem, Topol. Methods Nonlinear Anal., 1995, 6(1), 175–188
- [3] Cui Y., Sun J., Zou Y., Global bifurcation and multiple results for Sturm-Liouville problems, J. Comput. Appl. Math., 2011, 235(8), 2185–2192 http://dx.doi.org/10.1016/j.cam.2010.10.014
- [4] DeVore R.A., Lorentz G.G., Constructive Approximation, Grundlehren Math. Wiss., 303, Springer, Berlin, 1993 http://dx.doi.org/10.1007/978-3-662-02888-9
- [5] Erbe L., Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems, Math. Comput. Modelling, 2000, 32(5–6), 529–539 http://dx.doi.org/10.1016/S0895-7177(00)00150-3
- [6] Granas A., Guenther R.B., Lee J.W., On a theorem of S. Bernstein, Pacific J. Math., 1978, 74(1), 67–82 http://dx.doi.org/10.2140/pjm.1978.74.67
- [7] Granas A., Guenther R.B., Lee J.W., Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mountain J. Math., 1980, 10(1), 35–58 http://dx.doi.org/10.1216/RMJ-1980-10-1-35
- [8] Granas A., Guenther R.B., Lee J., Nonlinear Boundary Value Problems for Ordinary Differential Equations, Dissertationes Math. (Rozprawy Mat.), 244, Polish Acad. Sci. Inst. Math., Warsaw, 1985
- [9] Jentzen A., Neuenkirch A., A random Euler scheme for Carathéodory differential equations, J. Comput. Appl. Math., 2009, 224(1), 346–359 http://dx.doi.org/10.1016/j.cam.2008.05.060
- [10] Krasnoselskii M.A., The continuity of the operator fu(x) = f[x; u(x)], Doklady Akad. Nauk SSSR, 1951, 77(2), 185–188 (in Russian)
- [11] Krasnoselskii M.A., Topological Methods in the Theory of Nonlinear Integral Equations, International Series of Monographs on Pure and Applied Mathematics, 45, Pergamon Press, New York, 1964
- [12] Lorentz G.G., Bernstein Polynomials, Chelsea Publishing, New York, 1986
- [13] Rynne B.P., Second-order Sturm-Liouville problems with asymmetric, superlinear nonlinearities, Nonlinear Anal., 2003, 54(5), 939–947 http://dx.doi.org/10.1016/S0362-546X(03)00119-6
- [14] Rynne B.P., Second order, Sturm-Liouville problems with asymmetric, superlinear nonlinearities. II, Nonlinear Anal., 2004, 57(7–8), 905–916 http://dx.doi.org/10.1016/j.na.2004.03.021
- [15] Stengle G., Numerical methods for systems with measurable coefficients, Appl. Math. Lett., 1990, 3(4), 25–29 http://dx.doi.org/10.1016/0893-9659(90)90040-I
- [16] Stengle G., Error analysis of a randomized numerical method, Numer. Math., 1995, 70(1), 119–128 http://dx.doi.org/10.1007/s002110050113
- [17] Vainberg M.M., Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0323-8