Nonlinear BVPS with functional parameters

Existence of Solutions of Multi-Point BVPs for Impulsive Functional Differential Equations with Nonlinear Boundary Conditions

Two classes of multi-point BVPs for first order impulsive functional differential equations with nonlinear boundary conditions are studied. Sufficient conditions for the existence of at least one solution to these BVPs are established, respectively. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results. c ©2012 NGA. All rights reserved.

A New Method for Solving Nonlinear BVPs

As we know, the homotopy analysis method (HAM) provides us with a convenient way to adjust and control the convergence region and rate of the obtained series solutions. This great advantage of method is possible by finding a proper value of the so-called control parameter 0 c . In this paper, an efficient way of obtaining 0 c is proposed. Such value of parameter can be determined at the any ord...

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

Difference schemes for nonlinear BVPs on the half-axis

The scalar boundary value problem (BVP) du dx2 −mu = −f (x, u) , x ∈ (0,∞) , u (0) = μ1, lim x→∞ u (x) = 0, for a second order differential equation on the infinite interval [0,∞) is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme of which the solution coincides wit...

VARIABLE ORDER DIFFERENCE SCHEMES FOR NONLINEAR TWO-POINT BVPs

Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|m) w.r.t. the maximal step size |h|. This m-TDS represen...