Transcription of Solving ODE in MATLAB
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Solving ODE in MATLAB
Solving ODE in MATLAB . P. Howard Fall 2009. Contents 1 Finding Explicit Solutions 1. First Order Equations .. 2. Second and Higher Order Equations .. 3. Systems .. 3. 2 Finding Numerical Solutions 5. First-Order Equations with Anonymous Functions .. 5. First Order Equations with M-files .. 8. Systems of ODE .. 9. Passing Parameters .. 10. Second Order Equations .. 11. 3 Laplace Transforms 12. 4 Boundary Value Problems 12. 5 Event Location 13. 6 Numerical Methods 16. Euler's Method .. 16. Higher order Taylor Methods .. 20. 7 Advanced ODE Solvers 22. Stiff ODE .. 22. 1 Finding Explicit Solutions MATLAB has an extensive library of functions for Solving ordinary differential equations. In these notes, we will only consider the most rudimentary. 1. First Order Equations Though MATLAB is primarily a numerics package, it can certainly solve straightforward differential equations Suppose, for example, that we want to solve the first order differential equation y (x) = xy.
2 Finding Numerical Solutions MATLAB has a number of tools for numerically solving ordinary differential equations. We will focus on the main two, the built-in functions ode23 and ode45, which implement versions
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