Book 8 2 Background .1 Cosmology .11 Math Section 9.2

Book 9 Computational Mathematics Chapter 9 Ordinary Differential Equation Initial Value Problems

Section 1 Statement of bounday value problems

Let there be given the second order equation

(1.1)

The two-point boundary problem (B.V.P.) for Equation (1.1) looks for the function y = y(x) which inside a given interval [a,b] satisfies (1.1) and at a and b the boundary conditions

(1.2)

Consider the case when Equations (1.1) and (1.2) are linear and rewrite them in the form:

(1.3)

(1.4)

 

where p(x), q(x) and f(x) are continuous on the interval [a, b],

are given constants and

If A - B = 0, then the boundary conditions (1.4) are said to be uniform.The rnethods of approximate solution employ finite differences or analysis.