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<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Hello there,<o:p></o:p></span></font></p>
<p class=MyListing><span lang=EN-US><o:p> </o:p></span></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Here You have a quite general Newton-Raphson function.<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>Just fill function F(x) and use the code below. :]<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>good luck and best regards.<o:p></o:p></span></font></p>
<p class=MyListing><span lang=EN-US><o:p> </o:p></span></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>function y=F(x)<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> y=your formula;<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>endfunction<o:p></o:p></span></font></p>
<p class=MyListing><span lang=EN-US><o:p> </o:p></span></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'>function x1=NewtonRaphson(f,x0,Epsf,Epsx,h)<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> </span>x1=x0;<o:p></o:p></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> if h==[] then, h=1e-10; end; //step for
numerical derivative computation<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> while abs(f(x1))>Epsf | abs(x1-x0)>Epsx
do //checking the condition to finish iterations<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> x0=x1;
<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> df=(f(x0+h)-f(x0-h))/(2.0*h); //numerical
derivative (central scheme)<o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span lang=EN-US
style='font-size:10.0pt'> </span>x1=x0-f(x0)/df; <o:p></o:p></font></p>
<p class=MyListing><font size=2 face="Courier New"><span style='font-size:10.0pt'>
end <o:p></o:p></span></font></p>
<p class=MyListing><font size=2 face="Courier New"><span style='font-size:10.0pt'>endfunction<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>x0 = starting value,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>Epsf=0.0000000001; <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>Epsx=0.00000001;<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>h=0.0000000001;<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span lang=EN-US
style='font-size:12.0pt'>solution=NewtonRaphson(F,x0,Epsf,Epsx,h);</span></font><font
size=2 face=Arial><span lang=EN-US style='font-size:10.0pt;font-family:Arial'><o:p></o:p></span></font></p>
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