Functional continuous Runge–Kutta methods with reuse

Applied Numerical Mathematics - Tập 146 - Trang 165-181 - 2019
Alexey S. Eremin1
1Department of Information Systems, Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 Russia

Tài liệu tham khảo

Bellen, 2003 Bellen, 2009, Recent trends in the numerical solution of retarded functional differential equations, Acta Numer., 1, 10.1017/S0962492906390010 Bellmann, 1965, On the computational solution of a class of functional differential equations, J. Math. Anal. Appl., 12, 495, 10.1016/0022-247X(65)90017-X Eremin, 2016, Functional continuous Runge–Kutta–Nyström methods, Electron. J. Qual. Theory Differ. Equ., Proc. 10'th Coll. Qualitative Theory of Diff. Equ., 11, 1 Eremin, 2015, Efficient accurate non-iterative breaking point detection and computation for state-dependent delay differential equations, AIP Conf. Proc., 1648, 10.1063/1.4912436 Gelfand, 2000 Guglielmi, 2008, Computing breaking points in implicit delay differential equations, Adv. Comput. Math., 29, 229, 10.1007/s10444-007-9044-5 Hale, 1993, Introduction to Functional Differential Equations, vol. 99 Humphries, 2012, Singly diagonally implicit Runge–Kutta methods for state-dependent DDEs with overlapping Magpantay, 2011 Maset, 2005, Runge–Kutta methods for retarded functional differential equations, Math. Models Methods Appl. Sci., 15, 1203, 10.1142/S0218202505000716 Owren, 1992, Derivation of efficient continuous explicit Runge–Kutta methods, SIAM J. Sci. Stat. Comput., 13, 1488, 10.1137/0913084 Paul, 1994 Pimenov, 2001, General linear methods for the numerical solution of functional-differential equations, Differ. Equ., 37, 116, 10.1023/A:1019232718078 Tavernini, 1971, One-step methods for the numerical solution of Volterra functional differential equations, SIAM J. Numer. Anal., 8, 786, 10.1137/0708072 Tuzov