We discuss the construction of finite difference schemes for the two-point nonlinear boundary value problem:y
(2n)+f(x,y)=0,y
(2j)(a)=A
2j
,y
(2j)(b)=B
2j
,j=0(1)n−1,n≧2. In the case of linear differential equations, these finite difference schemes lead to (2n+1)-diagonal linear systems. We consider in detail methods of orders two, four and six for two-point boundary value problems involving a fourth order differential equation; convergence of these methods is established and illustrated by numerical examples.

Finite difference methods for two-point boundary value problems involving high order differential equations

The numerical solution of special eighth-order boundary value porblems by the modified decomposition method

Numerical methods for unilateral problems

In this report we survey numerical techniques of order 2, 4 and 6 for the solution of a two-point boundary value problem associated with a fourth-order linear ordinary differential equation. A sufficient condition guaranteeing a unique solution of the boundary value problem is also given. Numerical results are tabulated for two typical numerical examples and compared with some known methods including the shooting technique employing the classical fourth-order Runge-Kutta method.

Discrete methods for boundary value problems with applications in plate deflection theory

A new finite difference scheme with minimal phase-lag, for the numerical solution of fourth-order differential equations is developed in this paper. Numerical and theoretical results show that this new approach is more efficient compared with previously derived methods.

A new method for the numerical solution of fourth-order BVP's with oscillating solutions

An O(h6) Finite Difference Analogue for the Solution of Some Differential Equations Occurring in Plate Deflection Theory

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An O(h6) Finite Difference Analogue for the Solution of Some Differential Equations Occurring in Plate Deflection Theory