MATLAB Mathematics - SERC - Index of

5 Differential Equations
Initial Value Problems for ODEs and DAEs
This section describes how to use MATLAB to solve initial value problems
(IVPs) of ordinary differential equations (ODEs) and differential-algebraic
equations (DAEs). This section covers the following topics:
• “ODE Function Summary” on page 5-2
• “Introduction to Initial Value ODE Problems” on page 5-4
• “Solvers for Explicit and Linearly Implicit ODEs” on page 5-5
• “Examples: Solving Explicit ODE Problems” on page 5-9
• “Solver for Fully Implicit ODEs” on page 5-15
• “Example: Solving a Fully Implicit ODE Problem” on page 5-16
• “Changing ODE Integration Properties” on page 5-17
• “Examples: Applying the ODE Initial Value Problem Solvers” on page 5-18
• “Questions and Answers, and Troubleshooting” on page 5-43
ODE Function Summary
ODE Initial Value Problem Solvers
The following table lists the initial value problem solvers, the kind of problem
you can solve with each solver, and the method each solver uses.
Solver Solves These Kinds of Problems Method
ode45 Nonstiff differential equations Runge-Kutta
ode23 Nonstiff differential equations Runge-Kutta
ode113 Nonstiff differential equations Adams
ode15s Stiff differential equations and DAEs NDFs (BDFs)
ode23s Stiff differential equations Rosenbrock
ode23t
Moderately stiff differential equations and
DAEs
Trapezoidal
rule
5-2