DIFFEQN

DIFFEQN x0, y0, xf, maxseg, maxerr, BYREF yf, BYREF errcode USE expr

Solving first-order differential equations using Runge-Kutta method.

expr : f(y,x) = dy/dx with start condition: y(x = x0) = y0
x0, y0 : initial x, y
xf : final x
yf : result
maxseq : equivalent to precision
maxerr : maximum allowed error
errcode : 0 for success; otherwise calculation error

Example 1

' Solving dy/dx = 7*y^2 * x^3 with start condition y(2) = 3 

def f1(x,y) = 7*y^2 * x^3

y0 = 3
x0 = 2
yf = 0
xf = 1 
maxseg = 10000
maxerr = 0.001
errcode = 0

diffeqn x0, y0, xf, maxseg, maxerr, yf, errcode USE f1(x,y)

' Exact solution for comparision
def g1(x) = -1 / (7/4 * x^4 - 85/3)

print "g1(xf) = "; g1(xf)
print "yf(xf) = "; yf

if(errcode != 0) then
    print "Error solving equation"
    print "Increasing maxseg might help"
endif

Example 2

' Defining the differential equation for a stiffness system

def f2(y,t) = -1000*y + 3000 - 2000 * exp(-t)

' Solving equation at time tf = 0.001 seconds with y(0) = 0
y0 = 0
t0 = 0
yf = 0
tf = 0.001 
maxseg = 1000
maxerr = 0.001
errcode = 0

diffeqn t0, y0, tf, maxseg, maxerr, yf, errcode USE f2(y,t)

' Exact solution for comparision
def g2(t) = 3 - 0.998*exp(-1000*t) - 2.002 * exp(-t)

print "g2(tf) = "; g2(tf)
print "yf(tf) = "; yf

if(errcode != 0) then
    print "Error solving equation"
    print "Increasing maxseg might help"
endif

ABS ABSMAX ABSMIN ACOS ACOSH ACOT ACOTH ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATAN2 ATANH ATN CEIL COS COSH COT COTH CSC CSCH DEG DERIV DETERM DIFFEQN EXP EXPRSEQ FIX FLOOR FRAC INT INTERSECT INVERSE LINEQN LOG LOG10 M3APPLY M3IDENT M3ROTATE M3SCALE M3TRANS MAX MIN POLYAREA POLYCENT POLYEXT POW PTDISTLN PTDISTSEG PTSIGN RAD RND ROOT ROUND SEC SECH SEGCOS SEGLEN SEGSIN SEQ SGN SIN SINH SQR STATMEAN STATMEANDEV STATMEDIAN STATSPREADP STATSPREADS STATSTD SUM SUMSQ TAN TANH TRANSPOSE