{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "times" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 24 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 40 "Phase Portrait for a 3 \+ Dim Linear System" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restar t:\nwith(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Define the differential equat ion using parameters:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "L inDE := [diff(x(t),t) = a11*x(t)+a12*y(t)+a13*z(t),\n diff(y( t),t) = a21*x(t)+a22*y(t)+a23*z(t),\n diff(z(t),t) = a31*x(t) +a32*y(t)+a33*z(t)];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Input the values of the coefficients. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "a11:= 0; a12:= 3; a13:= 1;\na21:= 4; a22:= 1; a23:=-1;\na31:= \+ 2; a32:= 7; a33:=-5;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Input the inital conditions. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 302 "I C1:=[[x(0)=0.05,y(0)=0.05,z(0)=0.05],\n [x(0)=-0.05,y(0)=-0.05,z(0)=- 0.05],\n [x(0)=1.0,y(0)=-1.0,z(0)=-5.0],\n [x(0)=-1,y(0)=1,z(0)=5], \+ [x(0)=1.05,y(0)=-0.95,z(0)=-4.95],\n [x(0)=0.95,y( 0)=-1.05,z(0)=-5.05],\n [x(0)=-1.01,y(0)=0.99,z(0)=4.99],\n [x(0)=-0 .99,y(0)=1.01,z(0)=5.01]\n];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 " Plot the phaseportrait using Runge-Kutta method; the initial conditio ns are input on the line above and can be changed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "DEplot3d(LinDE, [x(t),y(t),z(t)], t=0..10, \n IC1,linecolour=BLUE, x=-5..5, y=-5..5, z=-5..5, stepsize=0.01,\n arrows=NONE, method=classical[rk4]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "A plot with more initial conditions." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 373 "IC2:=[\n [x(0)=0.05,y(0)=0.05,z(0)=0.05], \n [x(0)=-0.05,y(0)=-0.05,z(0)=-0.05], [x(0)=1.05,y(0)=-0.95,z(0 )=-4.95],\n [x(0)=0.95,y(0)=-1.05,z(0)=-5.0],\n [x(0)=-1.05,y(0)=0.9 5,z(0)=4.95],\n [x(0)=-0.95,y(0)=1.05,z(0)=5.0],\n [x(0)=2.05,y(0)=- 1.95,z(0)=0.05],\n [x(0)=1.95,y(0)=-2.05,z(0)=-0.05],\n [x(0)=-2.05, y(0)=1.95,z(0)=-0.05],\n [x(0)=-1.95,y(0)=2.05,z(0)=0.05]];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "DEplot3d(LinDE, [x(t),y(t),z(t)], t=0..1 0, \n IC2,linecolour=BLUE, x=-5..5, y=-5..5, z=-5..5, stepsize=0.01, \n arrows=NONE, method=classical[rk4]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }