/*-*-Macsyma-*-*/
/* 9:58pm  Thursday, 25 February 1982 -George Carrette. GJC@MIT-MC */

/* The RUNGE_KUTTA function solves:
 * A single first-order equation.
 * Simultaneous first-order equations.
 * A single secord-order equation.
 */

/* SETUP_AUTOLOAD(NDIFFQ,RUNGE_KUTTA,INIT_FLOAT_ARRAY)$ */
load("ndiffq")$

/* The equations */

DEFINE_VARIABLE(K,1.0,FLOAT,"Spring constant")$
DEFINE_VARIABLE(M,1.0,FLOAT,"mass")$

FX(TIME,STATE):=(MODE_DECLARE([TIME,ARRAY(STATE)],FLOAT), STATE[1])$
FV(TIME,STATE):=(MODE_DECLARE([TIME,ARRAY(STATE)],FLOAT), 
                 -K/M*STATE[0])$

ARRAY([T,X,V],FLOAT,10)$

/* Time step */

INIT_FLOAT_ARRAY(T,0.0,3.14159)$

/* Initial Condition */

(X[0]:0.0,V[0]:1.0)$

RUNGE_KUTTA([FX,FV],T,[X,V])$

GRAPH(T,[X,V],["*","+"])$

/* Another argument convention is to have a DEL-state vector passed in. */

FXV(DEL_STATE,TIME,STATE):=
 (MODE_DECLARE([TIME,ARRAY(DEL_STATE),ARRAY(STATE)],FLOAT),
  DEL_STATE[0]:STATE[1],
  DEL_STATE[1]:-K/M*STATE[0],
  'DONE)$

RUNGE_KUTTA(FXV,T,[X,V])$

GRAPH(T,[X,V],["*","+"])$