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| Syntax |
odestiff(function fval, order, ti, tout, ...maxstep, minstep, yi, eps, skip) |
| See Also | ode4rk , odepade |
d
-- y(t) = f(t, y(t))
dt
y(t) = yi at t = ti.
The integer scalar order
specifies the order of the backward difference method.
The real or double-precision scalar ti
specifies the initial value for t.
The row vector tout has the same type as ti
and specifies the values of t at which
odestiff should calculate the value of y.
The scalar maxstep has the same type as ti and
specifies the maximum step size in t.
The scalar minstep has the same type as ti and
specifies the minimum step size in t.
The column vector yi has the same type as ti
and specifies the initial value of y.
The column vector eps
has the same type and dimension as yi and
eps(i) is the desired accuracy for the
i-th element of y(t).
The integer scalar skip specifies the level of tracing inside of
odestiff.
If skip = 0, no tracing is done; otherwise,
the value of y(t) is printed at time
tout(skip), tout(2 skip) ... .
The return value for odestiff
has the same type and row dimension as yi,
the same number of columns as tout,
and its j-th column is the value of y at time tout(j).
(tin, yin, fout, dfout)
This function call sets fout
the value of f(tin, yin) and dfout to the value
d
-- f(tin, yin)
dy
f(t, y) with respect to the j-th element of y.
y'(t) = y (t) y (0) = 0
1 2 1
y'(t) = -y (t) y (0) = 1
2 1 2
y (t) = sin(t)
1
y (t) = cos(t)
2
clear
#
function fval(tin, yin, fout, dfout) begin
fout = {yin(2), -yin(1)}
dfout = {[0., 1.], [-1., 0.]}
return
end
order = 4
ti = 0.
tf = 2 * pi
maxstep = 1.
minstep = .01
yi = {0., 1.}
eps = {1e-4, 1e-4}
skip = 0
tout = seq(30)' * (tf - ti) / real(30)
yout = odestiff(function fval, order, ti, tout, ...
maxstep, minstep, yi, eps, skip)
gplot(tout', yout')
