MATLAB Mathematics - SERC - Index of

5 Differential Equations
2.5
Solution of van der Pol Equation, µ = 1000
2
1.5
1
0.5
solution y 1
0
−0.5
−1
−1.5
−2
−2.5
0 500 1000 1500 2000 2500 3000
time t
Example: Finite Element Discretization
fem1ode illustrates the solution of ODEs that result from a finite element
discretization of a partial differential equation. The value of N in the call
fem1ode(N) controls the discretization, and the resulting system consists of N
equations. By default, N is 19.
This example involves a mass matrix. The system of ODEs comes from a
method of lines solution of the partial differential equation
e – t ∂ -----
u =
∂t
∂ 2 ---------
u
∂x 2
with initial condition u( 0,
x) = sin( x)
and boundary conditions
ut0 ( , ) = utπ ( , ) = 0 . An integer N is chosen, h is defined as π ⁄ ( N + 1)
, and
5-22