PSTricks / Résolutions d'équations différentielles – (exemples)

ode01.tex [ retoursource ]

Conversion au format PDF de ode01.tex
    \psset{xunit=3, yunit=.4} 
    \begin{pspicture}(0,-1)(3,20)\psgrid 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{3}{2.71828182846 x exp} 
      \psplotequadiff[linecolor=magenta, plotpoints=16]{0}{3}{1}{} 
      \psplotequadiff[linecolor=blue, plotpoints=151]{0}{3}{1}{} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=15]{0}{3}{1}{} 
      \psplotequadiff[linecolor=Orange, method=rk4, plotpoints=4]{0}{3}{1}{} 
      \psset{linewidth=2\pslinewidth} 
      \rput*(3.3,19){\psline[linecolor=magenta](-.75cm,0)} 
      \rput*[l](3.3,19){\small\textsc{Euler} ordre 1 $h=0{,}2$} 
      \rput*(3.3,17){\psline[linecolor=blue](-.75cm,0)} 
      \rput*[l](3.3,17){\small\textsc{Euler} ordre 1 $h=0{,}02$} 
      \rput*(3.3,15){\psline[linecolor=red](-.75cm,0)} 
      \rput*[l](3.3,15){\small RK ordre 4 $h=0{,}2$} 
      \rput*(3.3,13){\psline[linecolor=Orange](-.75cm,0)} 
      \rput*[l](3.3,13){\small RK ordre 4 $h=1$} 
      \rput*(3.3,11){\psline[linecolor=green](-.75cm,0)} 
      \rput*[l](3.3,11){\small solution exacte} 
    \end{pspicture} 

ode02.tex [ retoursource ]

Conversion au format PDF de ode02.tex
    \def\Funct{neg} 
    \psset{xunit=1, yunit=8} 
    \begin{pspicture}(0,0)(10,1)\psgrid 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{10}{2.71828182846 x neg exp} 
      \psplotequadiff[linecolor=magenta, plotpoints=11]{0}{10}{1}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=101]{0}{10}{1}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=11]{0}{10}{1}{\Funct} 
      \rput*(3.3,.9){\psline[linecolor=magenta](-.75cm,0)} 
      \rput*[l](3.3,.9){\small\textsc{Euler} ordre 1 $h=1$} 
      \rput*(3.3,.8){\psline[linecolor=blue](-.75cm,0)} 
      \rput*[l](3.3,.8){\small\textsc{Euler} ordre 1 $h=0{,}1$} 
      \rput*(3.3,.7){\psline[linecolor=red](-.75cm,0)} 
      \rput*[l](3.3,.7){\small RK ordre 4 $h=1$} 
      \rput*(3.3,.6){\psline[linecolor=green](-.75cm,0)} 
      \rput*[l](3.3,.6){\small solution exacte} 
    \end{pspicture} 

ode03.tex [ retoursource ]

Conversion au format PDF de ode03.tex
    %\psset{xunit=3.2, showpoints=false} 
    \psset{xunit=6.4, yunit=9.6, showpoints=false} 
    %\begin{pspicture}(-2,-1)(2,2)\psgrid 
    \begin{pspicture}(0,1)(2,2)\psgrid 
      %\psplot[linewidth=4\pslinewidth,linecolor=lightgray]{-2}{-1.8}{x dup dup mul 4 exch sub sqrt add 2 div} 
      %\psplot[linewidth=4\pslinewidth,linecolor=lightgray]{-1.8}{1.8}{x dup dup mul 4 exch sub sqrt add 2 div} 
      \psplot[linewidth=4\pslinewidth,linecolor=lightgray]{0}{1.8}{x dup dup mul 4 exch sub sqrt add 2 div} 
      \psplot[linewidth=4\pslinewidth,linecolor=lightgray]{1.8}{2}{x dup dup mul 4 exch sub sqrt add 2 div} 
      \newcommand{\InitCond}{1} 
      \newcommand{\Func}{x mul 2 exch sub 4 x dup mul sub div} 
      \psplotequadiff[linecolor=magenta, plotpoints=11]{0}{1.9}{\InitCond}{\Func} 
      \psplotequadiff[linecolor=blue, plotpoints=101]{0}{1.9}{\InitCond}{\Func} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=11]{0}{1.9}{\InitCond}{\Func} 
    \end{pspicture} 

ode04.tex [ retoursource ]

Conversion au format PDF de ode04.tex
\psset{unit=4} 
\begin{pspicture}(-1,0)(3,2)\psgrid 
  \psplot[linewidth=4\pslinewidth,linecolor=gray]{-1}{3}{2.71828182846 x dup mul neg exp} 
  \psset{plotpoints=9} 
  \psplotequadiff[linecolor=cyan]{-1}{3}{1 2.71828182846 div}{x -2 mul mul} 
  \psplotequadiff[linecolor=yellow, method=RK4]{-1}{3}{1 2.71828182846 div}{x -2 mul mul} 
  \psset{plotpoints=21} 
  \psplotequadiff[linecolor=blue]{-1}{3}{1 2.71828182846 div}{x -2 mul mul} 
  \psplotequadiff[linecolor=Orange, method=RK4]{-1}{3}{1 2.71828182846 div}{x -2 mul mul} 
  \psset{linewidth=2\pslinewidth} 
  \rput*(2,1.7){\psline[linecolor=Orange](-1,0)} 
  \rput*[l](2,1.7){RK} 
  \rput*(2,1.8){\psline[linecolor=blue](-1,0)} 
  \rput*[l](2,1.8){\textsc{Euler}-1} 
  \rput*(2,1.9){\psline[linecolor=gray](-1,0)} 
  \rput*[l](2,1.9){solution} 
\end{pspicture} 

ode05.tex [ retoursource ]

Conversion au format PDF de ode05.tex
    \def\Funct{exch} 
    \psset{xunit=5, yunit=1.1} 
    \begin{pspicture}(0,0)(2,7)\psgrid 
      %%e^x 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{2}{2.71828182846 x exp} 
      \psplotequadiff[linecolor=magenta, plotpoints=11]{0}{2}{1 1}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=101]{0}{2}{1 1}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=11]{0}{2}{1 1}{\Funct} 
      %%ch(x) 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{2}{2.71828182846 dup x exp 
      exch x neg exp add 2 div} 
      \psplotequadiff[linecolor=magenta, plotpoints=11]{0}{2}{1 0}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=101]{0}{2}{1 0}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=11]{0}{2}{1 0}{\Funct} 
      %%sh(x) 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{2}{2.71828182846 dup x exp 
      exch x neg exp sub 2 div} 
      \psplotequadiff[linecolor=magenta, plotpoints=11]{0}{2}{0 1}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=101]{0}{2}{0 1}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=11]{0}{2}{0 1}{\Funct} 
      \rput*(2.1,1.9){\psline[linecolor=magenta](-.75cm,0)} 
      \rput*[l](2.1,1.9){\small\textsc{Euler} ordre 1 $h=1$} 
      \rput*(2.1,2.8){\psline[linecolor=blue](-.75cm,0)} 
      \rput*[l](2.1,2.8){\small\textsc{Euler} ordre 1 $h=0{,}1$} 
      \rput*(2.1,3.7){\psline[linecolor=red](-.75cm,0)} 
      \rput*[l](2.1,3.7){\small RK ordre 4 $h=1$} 
      \rput*(2.1,4.6){\psline[linecolor=green](-.75cm,0)} 
      \rput*[l](2.1,4.6){\small solution exacte} 
    \end{pspicture} 

ode06.tex [ retoursource ]

Conversion au format PDF de ode06.tex
    \def\Funct{exch neg} 
    \psset{xunit=1, yunit=5}%%4pi=12.5663706144 
    \def\quatrepi{12.5663706144} 
    \begin{pspicture}(0,-1)(\quatrepi,1)\psgrid 
      %%cos(x) 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{\quatrepi}{x 3.1415926 div 180 mul 
      cos} 
      %\psplotequadiff[linecolor=magenta, plotpoints=31]{0}{\quatrepi}{1 0}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=201]{0}{3.1415926}{1 0}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=31]{0}{\quatrepi}{1 0}{\Funct} 
      %%sin(x) 
      \psplot[linewidth=4\pslinewidth, linecolor=green]{0}{\quatrepi}{x 3.1415926 div 180 mul 
      sin} 
      %\psplotequadiff[linecolor=magenta, plotpoints=31]{0}{\quatrepi}{0 1}{\Funct} 
      \psplotequadiff[linecolor=blue, plotpoints=201]{0}{3.1415926}{0 1}{\Funct} 
      \psplotequadiff[linecolor=red, method=rk4, plotpoints=31]{0}{\quatrepi}{0 1}{\Funct} 
      \rput*(3.3,.9){\psline[linecolor=magenta](-.75cm,0)} 
      \rput*[l](3.3,.9){\small\textsc{Euler} ordre 1 $h=1$} 
      \rput*(3.3,.8){\psline[linecolor=blue](-.75cm,0)} 
      \rput*[l](3.3,.8){\small\textsc{Euler} ordre 1 $h=0{,}1$} 
      \rput*(3.3,.7){\psline[linecolor=red](-.75cm,0)} 
      \rput*[l](3.3,.7){\small RK ordre 4 $h=1$} 
      \rput*(3.3,.6){\psline[linecolor=green](-.75cm,0)} 
      \rput*[l](3.3,.6){\small solution exacte} 
    \end{pspicture} 

ode07.tex [ retoursource ]

Conversion au format PDF de ode07.tex
    \def\Func{exch 3.1415926 div 180 mul sin -9.8 mul} 
    \psset{yunit=2.5, xunit=4} 
    \begin{pspicture}(0,-2)(3,2)\psgrid 
      \psplot[linewidth=3\pslinewidth, linecolor=Orange]{0}{3}{x 3.1415926 div 180 mul 9.8 sqrt mul cos .1 mul} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=50]{0}{3}{.1 0}{\Func} 
      \psplot[linewidth=3\pslinewidth, linecolor=Orange]{0}{3}{x 3.1415926 div 180 mul 9.8 sqrt mul cos .25 mul} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=50]{0}{3}{.25 0}{\Func} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=50]{0}{3}{.5 0}{\Func} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=50]{0}{3}{1 0}{\Func} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=100]{0}{3}{3.1415926 2 div 0}{\Func} 
    \end{pspicture} 

ode08.tex [ retoursource ]

Conversion au format PDF de ode08.tex
    \psset{xunit=.7} 
    \begin{pspicture}(0,-4)(26,6)\psgrid 
      \psplot[plotpoints=200, linewidth=4\pslinewidth, linecolor=gray]{0}{26}{2.71828182846 x -8 div exp 
        x 127 sqrt 8 div mul 180 mul 3.1415926535 div dup cos 5 mul exch sin 127 sqrt div 5 
        mul add mul} 
      \psplotequadiff[linecolor=red, plotpoints=500]{0}{26}{5 0} 
      {dup 3 1 roll -4 div exch 2 mul sub} 
      \psplotequadiff[linecolor=blue, method=rk4, plotpoints=50]{0}{26}{5 0} 
      {dup 3 1 roll -4 div exch 2 mul sub} 
    \end{pspicture} 

 

Validation CSS Validation XHTMLJean-Michel Sarlat — Dernière modification : 26 juin 2008 (0.1s - 3781914 - vendredi 21 novembre 2008) vers le haut