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Author(s):
T. Watanbe, G. Gnudi
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Title:
A New Algorithm for Differential-Algebraic Equations Based on HIDM
Date of publication:
Feb. 1995
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Key words:
HIDM, differential-algebraic equations, stiff differential equations, symplectic integrator, time reversal integrator
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Abstract:
A new algorithm is proposed to solve differential-algebraic equations. The algorithm is an extension of the algorithm of general purpose HIDM(higher order implicit difference method). A computer program named HDMTDV and based on the new algorithm is constructed and its high performance is proved numerically through several numerical computations, including index-2 problem of differential-algebraic equations and connected rigid pendulum equations The new algorithm is also secular error free when applied to dissipationless dynamical systems. This nature is demonstrated numerically by computation of the Kepler motion. The new code can solve the initial value problem 0=L(psi(x), d psi(x)/dx, d^2psi(x)/dx^2, x), where L and psi are vectors of length N. The values of first or second derivatives of psi(x) are not always necessary in the equations.
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