Solving Ordinary Differential Equations Using Taylor Series
ACM Transactions on Mathematical Software (TOMS)
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
SIAM Journal on Scientific Computing
Numerical implementation of the exact dynamics of free rigid bodies
Journal of Computational Physics
Short Note: Reducing round-off errors in rigid body dynamics
Journal of Computational Physics
Accurate simple zeros of polynomials in floating point arithmetic
Computers & Mathematics with Applications
VSVO formulation of the taylor method for the numerical solution of ODEs
Computers & Mathematics with Applications
Choosing a stepsize for Taylor series methods for solving ODE'S
Journal of Computational and Applied Mathematics
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
ACM Transactions on Mathematical Software (TOMS)
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The integration of problems derived from dynamical systems is an important topic, both in mathematics and physics. In many publications, specific algorithms for each problem are proposed to obtain high accuracy in the integration. In this paper, we study the performance of the Taylor Series Method and the ways to obtain optimal accuracy in the integration of differential equations. We present different sources of rounding errors and how to reduce them. All the different strategies are compared to show their efficiency.