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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 .

method, xed-point iteration, Newton’s Method, or the Secant Method. The only di erence is that each evaluation of the function y(b;t), at a new value of t, is relatively expensive, since it requires the solution of an IVP over the interval [a;b], for which y0(a) = t. The value of that solution at

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