Non-Monotone Convergence Schemes

Abstract

We consider the second order BVP x″ = f (t, x, x′), x′(a) = A, x′(b) = B provided that there exist α and β (lower and upper functions) such that: β′ (α) < A < α′(a) and β′(b) < B < α′ (b). We consider monotone and non-monotone approximations of solutions to the Neumann problem. The results and examples are provided.

Keywords:

• nonlinear boundary value problem
• monotone iterations
• Neumann boundary condition
• non-monotone iterations

AMS Subject Classification:

• 34B15