technology_for_monte_carlo_simulation_maple数学建模.docVIP

Technology for Monte Carlo Simulation in Maple Using Monte Carlo simulation, find the approximate area under the curve y= cos (x) over the interval . Maple program: Area:=proc(expr::algebraic,an::numeric, bn::numeric, ymin::numeric, ymax::numeric,N::posint)option remember; local A,B,y1,y2,areaR,count,i,area,xpt,ypt,xrpt,yrpt,gen_x,gen_y,c1,c2,c3,c4,c5; y1:=ymin; y2:=ymax; A:=an; B:=bn; areaR:=(B-A)*(y2-y1); count:=0; i:=0; gen_x:=evalf(an+(bn-an)*rand(0..10^5)/10^5): gen_y:=evalf(ymin+(ymax-ymin)*rand(0..10^5)/10^5): xrpt:=[]: yrpt:=[]: while iN do Step 1 xpt[i]:=A+(B-A)*(rand()/10^12); ypt[i]:=y1+(y2-y1)*(rand()/10^12); Step 2 xrpt:=[op(xrpt),gen_x()]: yrpt:=[op(yrpt),gen_y()]: if ypt[i]evalf(f1(xpt[i])) then count:=count+1; i:=i+1; else i:=i+1; fi; od; area:=areaR*count/N; print(areaR,count,N,area); with(plots): c1:=pointplot(zip((x,y)-[x,y],xrpt,yrpt)): c2:=plot(expr,x=A..B, thickness=3): c3:=area: c4:=plot(y2,x=A..B,thickness=3, colour=red): c5:=plot(y1,x=A..B,thickness=3,colour=blue): display(c1,c2,c4,c5); end: Output: f1:= x-cos(x); f:=cos(x); Area(f,-1.57,1.57,0,2,2000); Real Area from the integral: int(f,x=-1.57..1.57);