{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 }{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 "R 3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Times" 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 11 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 153 " \+ \n\n \+ A SMALL EXAMPLE FOR THE USE OF \"STOCHPLOT6\" FOR MAPLE 6 " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 140 "CALLING \+ SEQUENCE: stochplot(s,t,p,z)\n\nstochplot plots a numerical solution u sing one of the schemes from the stochastic package for 1d SDEs\n" }} {PARA 0 "" 0 "" {TEXT -1 124 "INPUT:\n\ns: numerical scheme (as provid ed by the output of the \"Euler\", \"Milstein\" etc. Routines from the stochastic Package)" }}{PARA 0 "" 0 "" {TEXT -1 59 "h: time-step\np: \+ number of steps to compute\nz: initial value" }}{PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "read stochastic6;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read stochplot6V3;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(stochastic);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Construction of the Numerical Scheme..." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Euler([-(a*sin(x[ 1])+2*b*sin(2*x[1]))],[[sigma]]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5] ]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "\n ...and o utput of a point-trajectory using \"stochplot\"\n" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 71 "stochplot(Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[ 0.5]]), 0.1, 10, 1);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "\nSmaller time step and more steps\n" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "stochplot(Euler([-(1*sin(x[1 ])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 1);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Sa me times but different initial value" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "stochplot(Euler([-(1*sin( x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 10);" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Other schemes can be used the same way: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "milcomm([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]);" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "stochplot(m ilcomm([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 1);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "\nFor time dependent SDEs you can \+ use \"stochplot_time\":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 162 "CALLING SEQUENCE: stochplot_time(x,t,p,z)\n\nstochp lot_time plots a numerical solution using one of the schemes from the \+ stochastic package for 1d SDEs which may be" }}{PARA 0 "" 0 "" {TEXT -1 189 "time dependent, where time in the SDE should be written as \"t \" \n\nINPUT:\n\ns: numerical scheme (as provided by the output of the \"Euler\", \"Milstein\" etc. Routines from the stochastic Package)" } }{PARA 0 "" 0 "" {TEXT -1 59 "h: time-step\np: number of steps to comp ute\nz: initial value" }}{PARA 0 "" 0 "" {TEXT -1 17 "t0: initial time \n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "An \+ Example:" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 82 "stochplot_time(Euler([-(t*sin(x[1])+2*2*sin(2*x[1]) )],[[0.5]]), 0.01, 100, 10, 1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }