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Volume 16,     Number 4,     Winter 2008

 

ONE-STEP 4-STAGE
HERMITE-BIRKHOFF-TAYLOR DAE SOLVER
OF ORDER 12
TRUONG NGUYEN-BA, HAN HAO, HEMZA YAGOUB
AND RÉMI VAILLANCOURT

Abstract. The ODE solver HBT(12)4 [20] is expanded into the differential algebraic equation (DAE) solver, HBT(12)4DAE, for nonstiff and moderately stiff systems of fully implicit DAEs of arbitrarily high fixed index. Pryce's structural pre-analysis for DAEs is sketched. The stepsize is controlled by a local error estimator. Similarly, the Taylor series method of order 12, T12, and Dormand-Prince's DP(8,7)13M are expanded into T12DAE and DP(8,7)DAE, respectively, for DAEs. HBT(12)4DAE uses only the first nine derivatives of y as opposed to 12 for T12DAE. On the basis of the number of steps, CPU time, maximum global error and relative error at the end of the integration interval, HBT(12)4DAE is superior to DP(8,7)DAE, the super partitioned additive Runge- Kutta (SPARK), the pro jected implicit Runge-Kutta (PIRK), and methods based on Padé and Chebyshev series in solving several low- and high-index test DAEs.

 

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