Differential Equations › Section H · Boundary value problems and Fourier series › Topic H.8
Numerical methods for systems and boundary problems
Most equations met in engineering and science have no formula solution, and many come as systems or with conditions at two ends. The stepping methods you already know extend to systems almost unchanged, and two further ideas, shooting and finite differences, handle boundary value problems.
In this topic
- Beyond one equation and one starting point
- Systems and higher order equations
- Worked example: stepping a system
- Applied example: a ball with air resistance
- Why boundary problems are harder
- The shooting method
- Worked example: shooting
- Finite differences
- Worked example: a grid of four steps
- Software and validation
- Common mistakes to avoid
- Key takeaways
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