MATLAB Mathematics - SERC - Index of

Initial Value Problems for ODEs and DAEs
Examples: Solving Explicit ODE Problems
This section uses the van der Pol equation
2
y′′ 1 – µ ( 1 – y 1 ) y′ 1 + y 1 = 0
to describe the process for solving initial value ODE problems using the ODE
solvers.
• “Example: Solving an IVP ODE (van der Pol Equation, Nonstiff)” on page 5-9
describes each step of the process. Because the van der Pol equation is a
second-order equation, the example must first rewrite it as a system of first
order equations.
• “Example: The van der Pol Equation, m = 1000 (Stiff)” on page 5-12
demonstrates the solution of a stiff problem.
• “Evaluating the Solution at Specific Points” on page 5-15 tells you how to
evaluate the solution at specific points.
Note See “Basic ODE Solver Syntax” on page 5-7 for more information.
Example: Solving an IVP ODE (van der Pol Equation, Nonstiff)
This example explains and illustrates the steps you need to solve an initial
value ODE problem:
1 Rewrite the problem as a system of first-order ODEs. Rewrite the
van der Pol equation (second-order)
2
y′′ 1 – µ ( 1 – y 1 ) y′ 1 + y 1 = 0
where µ > 0 is a scalar parameter, by making the substitution y′ 1 = y 2 . The
resulting system of first-order ODEs is
y′ 1 = y 2
y′ 2 =
2
µ ( 1 – y 1 )y 2 – y 1
See “Working with Higher Order ODEs” on page 5-5 for more information.
5-9