A HIGHER ORDER MONOTONE ITERATIVE SCHEME FOR NONLINEAR NEUMANN BOUNDARY VALUE PROBLEMS

A Higher Order Monotone Iterative Scheme for Nonlinear Neumann Boundary Value Problems

The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.

Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales

Recently, periodic boundary value problems PBVPs for short for dynamic equations on time scales have been studied by several authors by using the method of lower and upper solutions, fixed point theorems, and the theory of fixed point index. We refer the reader to 1–10 for some recent results. In this paper we are interested in the existence of positive solutions for the following first-order P...

Positive Solutions and Monotone Iterative Sequences for a Class of Higher Order Boundary Value Problems of Fractional Order

In this paper, the method of lower and upper solutions is extended to deal with certain nonlinear fractional boundary value problem of order 3 < δ < 4. Two well-defined monotone sequences of lower and upper solutions which converge uniformly to actual solution of the problem are presented. The convergence of these sequences is verified numerically through one example and a result on the existen...

Numerical Solutions of Higher Order Nonlinear Boundary Value Problems by New Iterative Method

In this work, we present the approximate solutions of higher order nonlinear boundary value problems by an efficient numerical algorithm. The New Iterative Method (NIM) will by used to find such solutions. The solutions thus obtained by NIM, are in the form of rapidly convergent series. The approach developed is tested through examples, which gives the stability and efficiency of the proposed a...

Boundary value problems for higher order parabolicequationsRussell