Chapter 10
Boundary Value Problems for Ordinary Differential Equations
Boundary value problems specify conditions at different points rather than a complete initial state. This chapter develops shooting and finite-difference methods, explains fixed-value, derivative, and mixed boundary conditions, and extends the methods to eigenvalue problems. It introduces matrix formulations and Numerov integration, with physical applications in heat conduction, vibrations, and quantum mechanics.
In this chapter
- 10.1 Boundary value problems in physics
- 10.2 The shooting method
- 10.3 The finite difference method
- 10.4 Eigenvalue problems (physics emphasis)
- 10.5 Physics applications: worked examples
- 10.6 Practical guidelines for boundary value problems
- 10.7 Computational exercises and projects
Companion resources
Codes
Six programs in MATLAB, Python, C++, and Fortran: shooting with adaptive RKF45, linear finite differences, boundary-condition choices, nonlinear finite differences with Newton iteration, Numerov eigenvalue shooting, and a Schrödinger matrix problem.
View Chapter 10 codes →Exercises & Projects
Additional exercises on conditioning, boundary accuracy, nonlinear solutions, and eigenvalue searches, followed by physics projects beyond the book’s assigned problems.
View Chapter 10 exercises & projects →Resources
Benchmark solutions, method-selection guidance, numerical libraries for boundary value and matrix eigenvalue problems, and selected references.
View Chapter 10 resources →Updates & Errata
Draft clarifications, software notes, and corrections associated with Chapter 10 and its companion programs.
View Chapter 10 updates & errata →