TIDES: A free software based on the Taylor series method

• Autores: M. Rodríguez, Alberto Abad Medina , Roberto Barrio Gil , Fernando Blesa
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 35, 2011, págs. 83-95
• Idioma: inglés
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• Resumen

  • In many branches of the science, the numerical solution of differential equations is a natural request. However, the way to solve those equations is not always the same. Sometimes it is needed to solve the equation as fast as possible. In other cases good precision is required, even 100 digits or more to guarantee the final results.

    Sensitivity analysis also may be wanted in some integrators. In this paper, a new integration software based on the Taylor series method is introduced, with all these features. It can provide fast integrations that compete with well established codes and it is ready for high precision integrations with as many digits as desired.

    Besides it can compute the partial derivatives of the variables with respect to initial conditions or parameters of the system up to any order. This software has been written focusing in the philosophy easy-to-use, so with very simple commands the necessary code is generated automatically. At the end, we also present some numerical results to illustrate its competitiveness and high performance with chaotic problems.