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Unformatted text preview: 10.1: TWO-POINT BOUNDARY VALUE PROBLEMS KIAM HEONG KWA 1. Two-Point Boundary Value Problems Roughly speaking, a two-point boundary value problem consists of a differential equation together with suitable boundary conditions. The boundary conditions can either be specified values of the unknown func- tion y ( x ), of the derivative y ( x ) of the unknown function, or of a linear combination of y ( x ) and y ( x ) at two different points. This is to be dis- tinguished from an initial value problem in which the values of y ( x ) and y ( x ) are specified at the same point. A typical example of a two-point boundary value problem consists of a second-order differential equation y 00 + p ( x ) y + q ( x ) y = g ( x ) (1.1a) together with the boundary conditions ay ( ) + by ( ) = A, (1.1b) cy ( ) + dy ( ) = B, where p ( x ), q ( x ), and g ( x ) are functions on the interval [ , ], while a , b , c , d , A , and B are some prescribed values. The boundary value problem is called...
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