an:01487428
Zbl 0962.65057
Pasic, H.
An efficient method for solving implicit and explicit stiff differential equations
EN
Int. J. Numer. Methods Eng. 48, No. 1, 55-78 (2000).
0029-5981 1097-0207
2000
j
65L05 34A34 34A09 65L80 65L20
initial value problem; multibody dynamics; numerical examples; stiff systems; comparison of methods; Newton method; stability; differential-algebraic equations
This paper deals with an efficient algorithm which applies to both explicit as well as implicit ordinary differential equations. It differs from the traditional Runge-Kutta method. Using a polynomial of degree \(s\) for the solution \(y(x)\) leads to a nonlinear system which is solved by the Newton method. The formal precedure for uncoupling the algebraic system into a block-diagonal matrix with \(s\) blocks of size \(n\) is derived for any virtual number of stages \(s\).
The method may easily be constructed to be either \(A\)- or \(L\)-stable. In particular, for \(s= 3\) it has the same precision and stability properties as the well-known Runge-Kutta based Radau IIA method. Further, it may be considered as a good candidate for solving differential-algebraic equations of even higher index. Finally, the method is demonstrated by its application in the multibody dynamics.
I.Čomić (Novi Sad)