{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "de:=diff(y(t),t)=0.0 2225 *y(t) - 0.0003*y(t)^2; ic:= y(0)=25;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "dsolve(\{de,ic\},y(t));" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 627 " # Euler. Group 1, initialize.\n f:=(x,y) ->0.02225 *y - 0.0003*y^2; \n x0:=0:y0:=25:Dots:=[x0,y0]:n:=100:h:=25 0/n:\n # Group 2, repeat n times. Euler's method\n for i from 1 to n d o\n Y:=y0+h*f(x0,y0);\n x0:=x0+h:y0:=Y:Dots:=Dots,[evalf(x0),evalf(y 0)];\n od:\n # Group 3, display relevant dots and plot.\n Exact:=x->2 225/(30+59*exp(-89 *x/4000));\n P:=unapply(evalf(100*abs(exact-approx )/abs(exact)),(exact,approx)):\n m:=20:X:=[seq(1+m*j,j=0..n/m)]: # Li st of relevant indices\n print(\"Dots\"),seq(Dots[k],k=X);\n print( \"Exact\"),seq(Exact(Dots[k][1]),k=X);\n print(\"Error\"),seq(P(Exact (Dots[k][1]),Dots[k][2]),k=X);\n plot([Dots]);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }