MATH 134 -- Intensive Calculus for Science 2

April 19, 2002

An Euler's Method Example

We apply Euler's Method to approximate the solution of y ' = 3 - y

with y(0) = 1, using a step-size of h = .5

> restart;

> f:=(x,y)->3 - y;

> xpt[0]:=0: ypt[0]:=1:

> for i to 8 do

> ypt[i]:=ypt[i-1] + f(xpt[i-1],ypt[i-1])*(.5);

> xpt[i]:=xpt[i-1] + (.5);

> end do:

> points:=[seq([xpt[i],ypt[i]],i=0..8)];

> with(DEtools): with(plots):

Warning, the name changecoords has been redefined

> slopefield:=DEplot(diff(y(x),x)=3-y(x),y(x),x=-1..5,y=0..4):

> pointplot:=plot(points,color=black,style=point,symbol=circle):

> lineplot:=plot(points,color=black):

> display(pointplot,slopefield,lineplot);

Taking the step-size h even smaller would yield even better results.