Antitone operators and ordinary differential equations
A generalized quasilinearization technique is applied to obtain a sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with nonlocal discontinuous type integral boundary conditions.
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...