an:06271161
Zbl 1297.34017
Gulgowski, Jacek
Approximation of solutions to second order nonlinear Picard problems with Carath??odory right-hand side
EN
Cent. Eur. J. Math. 12, No. 1, 155-166 (2014).
00328695
2014
j
34A45 65L10 34B24
Picard problem; Kantorovich polynomial approximation; approximation of BVP solution
A method to approximate the solution of Picard second order two-point boundary value problems (BVP's) with Carath??odory right-hand side is presented. This method is based on the idea to replace the right-hand side by its Kantorovich polynomial, obtaining a sequence of another BVPs that approximate the original BVP. It is proved that if the original BVP has at least one essential solution, then there exists a sequence of approximate solutions converging to this solution. The approximated BVPs are transformed into finite dimensional problems such that the approximate solutions are expressed by using piecewise constant functions. Consequently, the solution of the original BVP is the limit of a sequence of piecewise constant functions.
Alexandru Mihai Bica (Oradea)