Euler's Method

dy/dx = cos(x)

y(0) = 0, step size of

>	with(plots):

>	solns:=array(1..33);

>	solns[1]:=(0,0):

>

y:=0:

>	for i from 2 to 33 do

>	y:=y+cos((i-2)*Pi/8)*Pi/8:solns[i]:=((i-1)*Pi/8,y):

>

end do:

>	solnss:=convert(solns,listlist):

>	EulerSoln:=pointplot(solnss,symbol=circle,symbolsize=12,color=red):

>	AnalyticalSoln:=plot(sin(x),x=0..4*Pi,thickness=3,color=blue):

>	display(EulerSoln,AnalyticalSoln);

y(0) = 0, step size

>	solns2:=array(1..65);

>	solns2[1]:=(0,0):

>

y:=0:

>	for i from 2 to 65 do

>	y:=y+cos((i-2)*Pi/16)*Pi/16:solns2[i]:=((i-1)*Pi/16,y):

>

end do:

>	solns2s:=convert(solns2,listlist):

>	EulerSoln:=pointplot(solns2s,symbol=circle,symbolsize=12,color=red):

>	AnalyticalSoln:=plot(sin(x),x=0..4*Pi,thickness=3,color=blue):

>	display(EulerSoln,AnalyticalSoln);

y(0) = 1, step size

>	solns3:=array(1..65);

>	solns3[1]:=(0,1):

>

y:=1:

>	for i from 2 to 65 do

>	y1:=y;y:=y1+cos((i-2)*Pi/16)*Pi/16;solns3[i]:=((i-1)*Pi/16,y);

>

end do:

>	solns3[15];

>	solns3s:=convert(solns3,listlist):

>	EulerSoln:=pointplot(solns3s,symbol=circle,symbolsize=12,color=red):

>	AnalyticalSoln:=plot(sin(x)+1,x=0..4*Pi,thickness=3,color=blue):

>	display(EulerSoln,AnalyticalSoln);

>