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{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 }
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