GNU Octave - Local Sector 7 web page

Chapter 23: Differential Equations 191function xdot = f (x, t)xdot = zeros (3,1);xdot(1) = 77.27 * (x(2) - x(1)*x(2) + x(1) \- 8.375e-06*x(1)^2);xdot(2) = (x(3) - x(1)*x(2) - x(2)) / 77.27;xdot(3) = 0.161*(x(1) - x(3));endfunctionand the initial condition x0 = [ 4; 1.1; 4 ], the set of equations can be integrated usingthe commandt = linspace (0, 500, 1000);y = lsode ("f", x0, t);If you try this, you will see that the value of the result changes dramatically between t= 0 and 5, and again around t = 305. A more efficient set of output points might bet = [0, logspace (-1, log10(303), 150), \logspace (log10(304), log10(500), 150)];See Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, inScientific Computing, R. S. Stepleman, editor, (1983) for more information about the innerworkings of lsode.23.2 Differential-Algebraic EquationsThe function daspk can be used to solve DAEs of the form0 = f(ẋ, x, t), x(t = 0) = x 0 , ẋ(t = 0) = ẋ 0using Petzold’s DAE solver Daspk.[x, xdot, istate, msg] = daspk (fcn, x 0, xdot 0, t, t crit)Solve the set of differential-algebraic equationsLoadable Function0 = f(x, ẋ, t)withx(t 0 ) = x 0 , ẋ(t 0 ) = ẋ 0The solution is returned in the matrices x and xdot, with each row in the resultmatrices corresponding to one of the elements in the vector t. The first element of tshould be t 0 and correspond to the initial state of the system x 0 and its derivativexdot 0, so that the first row of the output x is x 0 and the first row of the outputxdot is xdot 0.The first argument, fcn, is a string that names the function to call to compute thevector of residuals for the set of equations. It must have the form