Exact finite-difference methods based on nonlinear means

References

• Bildik , N. and Inç , M. 2003 . On the numerical solution of initial value problems for nonlinear trapezoidal formulas with different types . Int. J. Comput. Math. , 80 : 1175 – 1188 .
   Web of Science ®Google Scholar
• Bullen , P.S. 2003 . Handbook of Means and Their Inequalities , 2nd ed. , Dordrecht : Kluwer .
   Google Scholar
• Comtet , L. 1974 . Advanced Combinatorics: The Art of Finite and Infinite Expansions , Berlin : Springer Verlag .
   Google Scholar
• Corless , R.M. , Gonnet , G.H. , Hare , D.E.G. , Jeffrey , D.J. and Knuth , D.E. 1996 . On the Lambert W function . Adv. Comput. Math. , 5 : 329 – 359 .
   Web of Science ®Google Scholar
• Evans , D.J. 1989 . New Runge–Kutta methods for initial value problems . Appl. Math. Lett. , 2 : 25 – 28 .
   Google Scholar
• Evans , D.J. and Sanugi , B.B. 1987 . A comparison of numerical ODE solvers based on arithmetic and geometric means . Int. J. Comput. Math. , 23 : 37 – 62 .
   Web of Science ®Google Scholar
• Evans , D.J. and Sanugi , B.B. 1991 . A comparison of nonlinear trapezoidal formulae for solving initial-value problems . Int. J. Comput. Math. , 41 : 65 – 79 .
   Web of Science ®Google Scholar
• Foster , D.M.E. and Phillips , G.M. 1984 . A generalization of the Archimedean double sequence . J. Math. Anal. Appl. , 101 : 575 – 581 .
   Web of Science ®Google Scholar
• Gander , J.J. and Meyer-Spasche , R. 2000 . “ An introduction to numerical integrators preserving physical properties ” . In Applications of Nonstandard Finite Difference Schemes , Edited by: Mickens , R.E. 181 – 246 . Singapore : World Scientific .
   Google Scholar
• Meyer-Spasche , R. 1998 . Difference schemes of optimum degree of implicitness for a family of simple ODEs with blow-up solutions . J. Comput. Appl. Math. , 97 : 137 – 152 .
   Google Scholar
• Meyer-Spasche , R. 2007 . On difference schemes for quasilinear evolution problems . Electron. Trans. Numer. Anal. , 27 : 78 – 93 .
   Google Scholar
• Mickens , R.E. 1988 . Difference equation models of differential equations . Math. Comput. Modelling , 11 : 528 – 530 .
   Web of Science ®Google Scholar
• Mickens , R.E. 1994 . Nonstandard Finite Difference Models of Differential Equations , Singapore : World Scientific .
   Google Scholar
• Murugesan , K. , Dhayabaran , D.P. , Amirtharaj , E.C.H. and Evans , D.J. 2003 . Numerical strategy for the system of second order IVPs using RK method based on centroidal mean . Int. J. Comput. Math. , 80 : 233 – 241 .
   Web of Science ®Google Scholar
• Natalini , P. and Ricci , P. E. 2004 . An extension of the Bell polynomials . Comput. Math. Appl. , 47 : 719 – 725 .
   Web of Science ®Google Scholar
• Patidar , K. C. 2005 . On the use of nonstandard finite difference methods . J. Diff. Equations Appl. , 11 : 735 – 758 .
   Web of Science ®Google Scholar
• Toader , S. 2002 . Derivatives of generalized means . Math. Ineq. Appl. , 5 : 517 – 523 .
   Web of Science ®Google Scholar
• Villatoro , F. R. 2004 . Nonlinear trapezoidal methods based on logarithmic, Stolarsky's identric, and Seiffert's P and T means . WSEAS Trans. Syst. , 3 : 2656 – 2664 .
   Google Scholar
• Wazwaz , A.-M. 1994 . A comparison of modified Runge–Kutta formulas based on a variety of means . Int. J. Comput. Math. , 50 : 105 – 112 .
   Web of Science ®Google Scholar
• Wazwaz , A.-M. 1994 . On the numerical solution of y′ = f(x,y) by a class of nonlinear trapezoidal formulas . Int. J. Comput. Math. , 51 : 229 – 238 .
   Web of Science ®Google Scholar
• Wolfram , S. 2003 . The Mathematica Book , 5th ed. , Cambridge : Cambridge University Press .
   Google Scholar