#14 - 17

The problem involves the following information

> MODEL := diff( v(t) , t ) = ( exp(-0.1*t) - v(t) ) / 0.2 ; # define the differential equation model

> DOMAIN:= t = 0 .. 10 ;

> Nsteps := 10; # this makes dt=1.0

> ptsEa := Euler( MODEL, v(0)=0, DOMAIN, Nsteps ); # with NSTEPS= 4, we have dt=1.0

> ptsEb := Euler( MODEL, v(0)=2, DOMAIN, Nsteps ); # with NSTEPS= 4, we have dt=1.0

> ptsEc := Euler( MODEL, v(0)=-2, DOMAIN, Nsteps ); # with NSTEPS= 4, we have dt=1.0

> ptsEd := Euler( MODEL, v(0)=4, DOMAIN, Nsteps ); # with NSTEPS= 4, we have dt=1.0

> plotE4 := plot( [ptsEa,ptsEb,ptsEc,ptsEd], color = [GREEN,CYAN,BLUE,RED], title="Nsteps=10" ):

> plotE4;

Note the scale of the vertical axis. These solutions all appear to be growing at a tremendous rate! To see if this is real, let's recompute the Euler results with more steps. Let's double Nsteps to 20, i.e., cut dt in half (to dt=0.5)

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The magnitude is somewhat diminished but the solutions are still very rough (they should be smooth). Let's double Nsteps to 40 (i.e., dt=0.25).

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This looks better but is still rather jagged at the beginning. Let's repeat with Nsteps=80 (dt=0.125).

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This looks smooth. The point of this exercise was to find a reasonable number of steps to use in Euler's method.

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