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