2018/04/10 by Antonio Baeza, Sebastiano Boscarino, Baeza, Antonio +8
Mathematics · Engineering · #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics
paper · pdf · doi:10.48550/arxiv.1804.03627
In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method\nfor the numerical solution of ODEs is presented.\n This methods can be regarded as an approximate formulation of the Taylor\nmethods and it follows an approach that has a much easier implementation than\nthe original Taylor methods, since only the functions in the ODEs, and not\ntheir high order derivatives, are needed. In this reference, the absolute\nstability region of the new methods is conjectured to be coincident with that\nof their exact counterparts. There is also a conjecture about their\nrelationship with Runge-Kutta methods. In this work we answer positively both\nconjectures.\n