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The Shooting Method for Two-Point Boundary Value …

Jim LambersMAT 461/561 Spring Semester 2009-10 Lecture 25 NotesThese notes correspond to Sections and in the Shooting Method for Two-Point Boundary Value ProblemsWe now consider thetwo-point Boundary Value problem(BVP) = ( , , ), < < ,a second-order ODE, withboundary conditions ( ) = , ( ) = .This problem is guaranteed to have a unique solution if the following conditions hold: , , and are continuous on the domain ={( , , ) , < < , < < }. >0 on is bounded on .There are several approaches to solving this type of problem. The first Method that we willexamine is called theshooting Method .

as a system of rst-order equations before it can be solved by standard numerical methods such as Runge-Kutta or multistep methods. In the case where y00 = f(x;y;y0) is a linear ODE, selecting the slope tis relatively simple.Let

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