TIDES
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS. We present a new free software called TIDES, based on the classical Taylor series method and using an optimized variable-stepsize variable-order formulation. This software, developed by A. Abad, R Barrio, F. Blesa, M. Rodriguez, (GME), consists on a library on C and FORTRAN and a precompiler done in MATHEMATICA that creates a C or a FORTRAN program that permits to compute up to any precision level (by using multiple precision libraries for high precision when needed) the solution of an ODE system. The software has been done to be extremely easy to use. The program also permits to compute in a direct way not only the solution of the differential system, but also the partial derivatives, up to any order, of the solution with respect to the initial conditions or any parameter of the system. This is based on the extended Taylor series method for sensitivity analysis.
Keywords for this software
References in zbMATH (referenced in 25 articles , 2 standard articles )
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- Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M.: Automatic implementation of the numerical Taylor series method: a \textscMathematicaand \textscSageapproach (2015)
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- Groza, Ghiocel; Razzaghi, Mohsen: A Taylor series method for the solution of the linear initial-boundary-value problems for partial differential equations (2013)
- Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodríguez, Marcos: Algorithm 924, TIDES, a Taylor series integrator for differential equations (2012)
- Bailey, D. H.; Barrio, R.; Borwein, J. M.: High-precision computation: mathematical physics and dynamics (2012)