Order conditions for General Linear Nyström methods

[1]  Raffaele D'Ambrosio,et al.  Numerical search for algebraically stable two-step almost collocation methods , 2013, J. Comput. Appl. Math..

[2]  R. D'Ambrosio,et al.  General linear methods for y′′ = f (y (t)) , 2012, Numerical Algorithms.

[3]  Beatrice Paternoster,et al.  Two-step modified collocation methods with structured coefficient matrices , 2012 .

[4]  Raffaele D'Ambrosio,et al.  Exponentially fitted two-step hybrid methods for y″=f(x, y) , 2011, J. Comput. Appl. Math..

[5]  Raffaele D'Ambrosio,et al.  Construction and implementation of highly stable two-step continuous methods for stiff differential systems , 2011, Math. Comput. Simul..

[6]  J. Butcher,et al.  The tree and forest spaces with applications to initial-value problem methods , 2010 .

[7]  Ernst Hairer,et al.  Algebraic Structures of B-series , 2010, Found. Comput. Math..

[8]  Raffaele D'Ambrosio,et al.  Continuous two-step Runge–Kutta methods for ordinary differential equations , 2010, Numerical Algorithms.

[9]  John C. Butcher,et al.  Trees and numerical methods for ordinary differential equations , 2010, Numerical Algorithms.

[10]  J. Butcher.  B‐series and B‐series Coefficients , 2009 .

[11]  Zdzisław Jackiewicz,et al.  General Linear Methods for Ordinary Differential Equations: Jackiewicz/General Linear , 2009 .

[12]  John C. Butcher,et al.  General linear methods for ordinary differential equations , 2009, Math. Comput. Simul..

[13]  Beatrice Paternoster,et al.  Two-step hybrid collocation methods for y"=f(x, y) , 2009, Appl. Math. Lett..

[14]  Beatrice Paternoster,et al.  A General Family of Two Step Runge-Kutta-Nyström Methods for y" = f(x, y) Based on Algebraic Polynomials , 2006, International Conference on Computational Science.

[15]  Stephen Gilmore,et al.  Combining Measurement and Stochastic Modelling to Enhance Scheduling Decisions for a Parallel Mean Value Analysis Algorithm , 2006, International Conference on Computational Science.

[16]  Matematik,et al.  Numerical Methods for Ordinary Differential Equations: Butcher/Numerical Methods , 2005 .

[17]  C. Brouder,et al.  Trees, Renormalization and Differential Equations , 2004 .

[18]  Beatrice Paternoster,et al.  Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials , 2003, International Conference on Computational Science.

[19]  John P. Coleman,et al.  Order conditions for a class of two‐step methods for y″ = f (x, y) , 2003 .

[20]  J. Butcher,et al.  A New Approach to the Algebraic Structures for Integration Methods , 2002, BIT Numerical Mathematics.

[21]  N. Cong,et al.  Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs , 2002 .

[22]  Beatrice Paternoster,et al.  Two Step Runge-Kutta-Nyström Methods for y'' = f(x, y) and P-Stability , 2002, International Conference on Computational Science.

[23]  Beatrice Paternoster,et al.  Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials , 1998 .

[24]  A. Connes,et al.  Hopf Algebras, Renormalization and Noncommutative Geometry , 1998, hep-th/9808042.

[25]  Ernst Hairer,et al.  Order Conditions for General Two-Step Runge--Kutta Methods , 1997 .

[26]  John C. Butcher,et al.  Order conditions for two-step Runge-Kutta methods , 1997 .

[27]  E. Hairer,et al.  A theory for Nyström methods , 1975 .

[28]  Beatrice Paternoster,et al.  Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations , 2011, Math. Comput. Simul..

[29]  R. D'Ambrosio,et al.  Parameter estimation in exponentially fitted hybrid methods for second order differential problems , 2011, Journal of Mathematical Chemistry.

[30]  Beatrice Paternoster,et al.  Two-step almost collocation methods for ordinary differential equations , 2009, Numerical Algorithms.

[31]  Abraham OCHOCHE,et al.  General Linear Methods , 2006 .

[32]  B. Paternoster.  Two step Runge-Kutta-Nystrom methods based on algebraic polynomials , 2003 .

[33]  Jack Dongarra,et al.  Computational Science — ICCS 2003 , 2003, Lecture Notes in Computer Science.

[34]  J. van Leeuwen,et al.  Computational Science — ICCS 2002 , 2002, Lecture Notes in Computer Science.