Andrew Sommese 2004Adams-Bashforth two-stepn :=2;t:=vector(n): f:=vector(n):for i from 1 to n-1 do t[i]:= t[n]-(n-i)*h; od;z:=interp(t,f,x);int(z,x=t[n]..t[n]+h);expand(%);

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NiMsKiooLCYmSSJmRzYiNiMiIiMhIiImRic2IyIiIkYuRi5JImhHRihGKywmKiQsJiZJInRHRihGKUYuRi9GLkYqRi4qJEYzRipGK0YuI0YrRioqJkYmRi5GM0YuRisqJkYmRi5GL0YuRi4qJkYsRi5GM0YuRi4=NiMsJiomJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojIiIkRikqJiZGJjYjRipGKkYrRiojISIiRik=

automating this we have the Adams-Bashforth n-step method for n=1 to 7for n from 1 to 7 dot:=vector(n): f:=vector(n):for i from 1 to n-1 do t[i]:= t[n]-(n-i)*h: od:z:=interp(t,f,x):int(z,x=t[n]..t[n]+h):print(expand(%)): od:

NiMqJiZJImZHNiI2IyIiIkYoSSJoR0YmRig=NiMsJiomJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojIiIkRikqJiZGJjYjRipGKkYrRiojISIiRik=NiMsKComJkkiZkc2IjYjIiIkIiIiSSJoR0YnRiojIiNCIiM3KiYmRiY2IyIiI0YqRitGKiMhIiVGKSomJkYmNiNGKkYqRitGKiMiIiZGLg==NiMsKiomJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojIiNQIiNDKiYmRiY2I0YqRipGK0YqIyEiJCIiKSomJkYmNiMiIiRGKkYrRiojISNmRi4qJiZGJjYjIiIlRipGK0YqIyIjYkYuNiMsLComJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojISRQJyIkZyQqJiZGJjYjRipGKkYrRiojIiReIyIkPygqJiZGJjYjIiIkRipGK0YqIyIkNCIiI0kqJiZGJjYjIiIlRipGK0YqIyElKFEiRi4qJiZGJjYjIiImRipGK0YqIyIlLD5GNA==NiMsLiomJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojIiRmKiIkIVsqJiZGJjYjRipGKkYrRiojISMmKiIkKUcqJiZGJjYjIiIkRipGK0YqIyElXE8iJD8oKiYmRiY2IyIiJUYqRitGKiMiJSIqXEY7KiYmRiY2IyIiJkYqRitGKiMhJVRFRi4qJiZGJjYjIiInRipGK0YqIyIleFUiJVM5NiMsMComJkkiZkc2IjYjIiIjIiIiSSJoR0YnRiojISUuYyIlP0QqJiZGJjYjRipGKkYrRiojIiYoMz4iJiFbZyomJkYmNiMiIiRGKkYrRiojIic4ZDgiJmcsIyomJkYmNiMiIiVGKkYrRiojISZhMiIiJFgqKiYmRiY2IyIiJkYqRitGKiMiJyQ9TiNGOyomJkYmNiMiIidGKkYrRiojISZQJz1GLiomJkYmNiMiIihGKkYrRiojIidAKCk+RjQ=

Now for the implicit methods--first we do the Adams-Moulton 2-stepn :=2;t:=vector(n+1): f:=vector(n+1):for i from 1 to n+1 do t[i]:= tF-(n-i+1)*h; od;z:=interp(t,f,x):z:=int(z,x=tF-h..tF):expand(%); factor(%);

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NiMsJComSSJoRzYiIiIiLCgmSSJmR0YmNiMiIiMhIikmRio2I0YnRicmRio2IyIiJCEiJkYnIyEiIiIjNw==

automating this we have the Adams-Moulton n-step method for n=1 to 7for n from 1 to 7 dot:=vector(n+1): f:=vector(n+1):for i from 1 to n+1 do t[i]:= tF-(n-i+1)*h: od:z:=interp(t,f,x):z:=int(z,x=tF-h..tF):expand(%): factor(%): print(%):od:

NiMsJComSSJoRzYiIiIiLCYmSSJmR0YmNiMiIiNGJyZGKjYjRidGJ0YnI0YnRiw=NiMsJComSSJoRzYiIiIiLCgmSSJmR0YmNiMiIiMhIikmRio2I0YnRicmRio2IyIiJCEiJkYnIyEiIiIjNw==NiMsJComSSJoRzYiIiIiLComSSJmR0YmNiMiIiMhIiYmRio2I0YnRicmRio2IyIiJCIjPiZGKjYjIiIlIiIqRicjRiciI0M=NiMsJComSSJoRzYiIiIiLCwmSSJmR0YmNiMiIiMhJDEiJkYqNiNGJyIjPiZGKjYjIiIkIiRrIyZGKjYjIiIlISRZJyZGKjYjIiImISReI0YnIyEiIiIkPyg=NiMsJComSSJoRzYiIiIiLC4mSSJmR0YmNiMiIiMiJHQiJkYqNiNGJyEjRiZGKjYjIiIkISQjWyZGKjYjIiIlIiQpeiZGKjYjIiImISVGOSZGKjYjIiInISR2JUYnIyEiIiIlUzk=NiMsJComSSJoRzYiIiIiLDAmSSJmR0YmNiMiIiMiJTdqJkYqNiNGJyEkaikmRio2IyIiJCEmNi0jJkYqNiMiIiUiJi92JCZGKjYjIiImISZoayUmRio2IyIiJyImN14nJkYqNiMiIigiJigzPkYnI0YnIiYhW2c=NiMsJComSSJoRzYiIiIiLDImSSJmR0YmNiMiIiMhJl44IiZGKjYjRiciJXY4JkYqNiMiIiQiJipcVCZGKjYjIiIlISZaJikpJkYqNiMiIiYiJ0xKNyZGKjYjIiInIScoekAiJkYqNiMiIigiJ1wpUiImRio2IyIiKSImKnpPRicjRiciJ2c0Nw==