numerical solution of differential equations

[Ether]

Originally Posted by sspoldi

one forward Euler integration, one backward Euler integration

V_n+1 = V_n + A_n∙dt;
X_n+1 = X_n + V_n+1∙dt;

Maybe provides some insight: the above is algebraically equivalent to

V_n+1 = V_n + A_n∙dt;
X_n+1 = X_n + dt∙(V_n+V_n+1)/2 + ½∙A_n∙dt²