Programming Language:
    Complex Numbers | Linear Algebra | Fit Algorithms | Interpolation | Root Finding | ODE | FFT | Special Functions | Integration

    LINEAR DIFFERENTIAL EQUATIONS

    - Solving Linear Differential Equations with Xi -

    The routine ode_solve(func,y,t[,abs_tol][,rel_tol]) solves ordinary differential equations. func describes the equation, y contains an array of initial values at point t[0] and the array t represents the independent variable. The optional variables abs_tol and rel_tol are the absolute and the relative tolerance parameters. A nice example is the damped harmonic oszillator - in this case the differential equation y''+0.12*y'+y=0 with the initial conditions y[0]=0.7, y'[0]=1. Because ode_solve can solve equations of first order only you must translate this equation of second order into two equations of first order:

    y0'=y1
    y1'=-y0-0.12*y1
    
    Then You can input:
    (  1)>t=dincarr(1000)/30;
    (  2)>y=ode_solve([(y;t)->y':y'={y[1],-y[0]-0.12*y[1]};],{0.7,1},t);
    
    With
    (  3)>plot(t,y[0,*],\line);
    
    you obtain the following output (after reduction of the window):


    Rechts Index Index Index Linls © 1995 by Bodo Junglas, Klaus Spanderen and Fabian Weis
    - Last revised: April 23 1996