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Question: Numerical Integration Maplet ... need help.

Question:Numerical Integration Maplet ... need help.

Chad Salyer 4 Maple
assign algebra display format integral
November 29 2006
0
Im trying to author a maplet which executes numerical integration on a function for an interval. Here is what I have so far. This is a the part of the assignment that didn't require maplet format. (This part I got to work) restart; a:= 1; b := 3; f:=x->100/x^2*sin(10/x); L:=[];# which is list of lists ListOfEndPts:=[b]; found := false; MaxNoPasses:=70; tolerance:=1.0e-4; simpAB:=evalf(student[simpson](f(x),x=a..b,2));app:=0; for PassNo from 1 to MaxNoPasses while not found do print("**********************************************"); middle := (a+b)/2.0: print(`Pass number` = PassNo); print(`A` = a); print(`B` = b); print(`simpAB ` =simpAB); simpAM := evalf(student[simpson](f(x),x=a..middle,2)); simpMB := evalf(student[simpson](f(x),x=middle..b,2)); sum1:=simpAM + simpMB; print(`simpAM `=simpAM); print(`simpAM + simpMB `=sum1); Test:=abs(simpAB - (simpAM + simpMB)); print(`Test `=Test); if Test <> 0 then tail:=L[nops(L)]; a:=tail[1]: b:=tail[2]: simpAB:=tail[3]; L:=subsop(nops(L)=NULL,L); else found:=true; end if; else print("Split. Append [a,middle,SimpAM] to the list.Reset a to equal middle. Leave b alone"); L:=[op(L),[a,middle,simpAM]]; a:=middle; simpAB:=simpMB; print(`List `=L);print(`New a `=a,`New b `=b); print(`List of endpoints`=ListOfEndPts); print(`Approximation to date `=app); end if; end do: print(` List of SORTED end points `=ListOfEndPts); print(`Number of end points `=nops(ListOfEndPts)); app; L1:=evalf(map(f,ListOfEndPts)); L:=zip( (x,y)->[x,y],ListOfEndPts,L1); p1:=plots[pointplot](L,axes=BOXED,title="f(x) = 100/x^2*sin(10/x) on [1,3]"); p2:=plot(f(x),x=1..3); plots[display]([p1,p2]); Now what I need to do is construct a maplet that performs the same operation for given inputs. Here is the maplet.(Doesn't work) with(Maplets[Elements]): Numint:=proc() local f1,digits,L1,p1,p2,a,b,f,PassNo,middle,simpAM,simpAB,app,simpMB,Test,ListOfEndPts,sum1,tail,L,found,MaxNoPasses,tolerance,pass; L:=[]; ListOfEndPts:=[b]; found := false; pass:=0; digits:=Get(TFd::algebraic); a:=Get(TFa::algebraic); b:=Get(TFb::algebraic); f1:=Get(TFf::algebraic); f:=x->f1; MaxNoPasses:=Get(TFp::algebraic); tolerance:=Get(TFt::algebraic); simpAB:=evalf(student[simpson](f(x),x=a..b,2)); app:=0; for PassNo from 1 to MaxNoPasses while not found do pass:=pass + 1; middle := (a+b)/2.0: simpAM := evalf(student[simpson](f(x),x=a..middle,2)); simpMB := evalf(student[simpson](f(x),x=middle..b,2)); sum1:=simpAM + simpMB; Test:=abs(simpAB - (simpAM + simpMB)); if Test <> 0 then tail:=L[nops(L)]; a:=tail[1]: b:=tail[2]: simpAB:=tail[3]; L:=subsop(nops(L)=NULL,L); else found:=true; end if; else L:=[op(L),[a,middle,simpAM]]; a:=middle; simpAB:=simpMB; end if; end do: L1:=evalf(map(f,ListOfEndPts)); L:=zip( (x,y)->[x,y],ListOfEndPts,L1); p1:=plots[pointplot](L,axes=BOXED,title="f(x) = 100/x^2*sin(10/x) on [1,3]"); p2:=plot(f(x),x=1..3); ##plots[display]([p1,p2]);##set plotter value print(L1); print(L); Maplets:-Tools:-Set('TFapp'=evalf[digits](app)); Maplets:-Tools:-Set('TFmapapp'=int); Maplets:-Tools:-Set('TFpass'=pass); end proc: maplet1:=Maplet([[" f(x) = ",TextField['TFf'](value='100/x^2*sin(10/x)'),"Digits Accuracy =",TextField['TFd'](width=5,value='10'),"Tolerance =",TextField['TFt'](width=5,value='1.0e-4'),"Maximum number of iterations =",TextField['TFp'](width=5,value='100'),"a =",TextField['TFa'](width=5,value='1'),"b =",TextField['TFb'](width=5,value='3')],["Adaptive approximation of the integral =",TextField['TFapp'](value='0'),"Maple approximation of the integral =",TextField['TFmapapp'](value='0'),"Number of iterations =",TextField['TFpass'](width=5,value='0')],[Plotter['PL']()],[Button("Close", Shutdown(""))] ]): Maplets[Display](maplet1); Any advice or suggestions are greatly appreciated. Thanks.
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