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

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.