Approximation and existence of solutions for nonlinear two point BVPs of ordinary second order differential equations
In this paper, using the operator theoretic techniques, we present some algorithms for the existence and approximation of the solutions for a couple of Dirichlet and Neumann nonlinear two point boundary value problems of ordinary second order hybrid differential equations. The proof of the main results rely on the Dhage iteration principle embodied in some recent hybrid fixed point theorems of Dhage(2014) in a partially ordered normed linear space. The approximation of solutions of the considered BVPs of ordinary nonlinear hybrid differential equations are obtained under certain mixed partial continuity and partial compactness type conditions. Some numerical examples are also provided to illustrate the validity of our hypotheses and the abstract results.