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Applied Numerical Methods with MATLAB for Engineers and Scientists, 2/e
Steven C. Chapra, Tufts University
Boundary-Value Problems

Chapter Objectives

The primary objective of this chapter is to introduce you to solving boundary-value problems for ODEs. Specific objectives and topics covered are

1. Understanding the difference between initial-value and boundary-value problems

2. Knowing how to express an nth-order ODE as a system of n first-order ODEs.

3. Knowing how to implement the shooting method for linear ODEs by using linear interpolation to generate accurate “shots.”

4. Understanding how derivative boundary conditions are incorporated into the shooting method.

5. Knowing how to solve nonlinear ODEs with the shooting method by using root location to generate accurate “shots.”

6. Knowing how to implement the finite-difference method.

7. Understanding how derivative boundary conditions are incorporated into the finite-difference method.

8. Knowing how to solve nonlinear ODEs with the finite-difference method by using root location methods for systems of nonlinear algebraic equations.








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