Capitolul 1 Ecuatii diferentiale de ordinul ˆıntâi rezolvabile prin ...

142 CAPITOLUL 4
k3:=f1(t(n-1,h)+h/2,x1(n-1,h)+h*k2/2,x2(n-1,h)+h*k2/2);
k4:=f1(t(n-1,h)+h/2,x1(n-1,h)+h*k3,x2(n-1,h)+h*k3);
x1(n-1,h)+h/6*(k1+2*k2+2*k3+k4)
> end if;
> end proc:
> x2:=proc(n,h) local m1,m2,m3,m4;
> if n=0 then x2(0) else
m1:=f2(t(n-1,h),x1(n-1,h),x2(n-1,h));
m2:=f2(t(n-1,h)+h/2,x1(n-1,h)+h*m1/2,x2(n-1,h)+h*m1/2);
m3:=f2(t(n-1,h)+h/2,x1(n-1,h)+h*m2/2,x2(n-1,h)+h*m2/2);
m4:=f2(t(n-1,h)+h/2,x1(n-1,h)+h*m3,x2(n-1,h)+h*m3);
x2(n-1,h)+h/6*(m1+2*m2+2*m3+m4)
> end if;
> end proc:
> x1(0):=1: x2(0):=1:
> x1(t):=[seq(x1(i,h),i=0..n)];
x1 (t) := [1., 1.75588586516103406, 2.67099024240189342,
3.82829207712650410, 5.33273206041661840,
7.32072833903442266, 9.97254650756094564,
13.5286455567960680, 18.3114819804437801,
24.7547491716790910, 33.4427034511831920]
> x2(t):=[seq(x2(i,h),i=0..n)];
x2 (t) := [1., 1.24835204296884550, 1.60990093931829237,
2.11743086851170714, 2.81696313624160988,
3.77192924966291354, 5.06892269795481632,
6.82555099257945131, 9.20109996691309817,
12.4109773422481773, 16.7462452598074308]
> t:=[seq(t(i,h),i=0..n)];
t := [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
> sol_x1:=5/3*exp(3*t)-2/3*exp(-3*t):
> sol_x2:=5/6*exp(3*t)+1/6*exp(-3*t):
> eval(sol_x1(t),t=0);
eval(sol_x1(t),t=0.1);eval(sol_x1(t),t=0.2);