The uniqueness of solutions to discrete, vector, two-point boundary value problems

The uniqueness of solutions to discrete, vector, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented. c...

Solvability of Discrete Two-point Boundary Value Problems

We study the discrete approximation to solutions of first-order system arising from applying the trapezoidal rule to a second-order scalar ordinary differential equation. In the trapezoidal rule the finite difference approximation are Dyk = (zk + zk−1)/2, Dzk = ( fk + fk−1)/2, for k = 1, 2, .., n, and tk = kh for k = 0, ..., n, 0 = G ( (y0, yn), (z0 + z1)/2, (zn−1 + zn)/2) ) , where fi ≡ f (ti,...

B-SPLINE METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation