Monotone scheme for nonlinear first-order hyperbolic initial-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.

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

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...

First Order Initial Value Problems

where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys

First Order Initial Value Problems

where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys