PUBLICATIONS:

[138] BUTCHER, J. C. ‘Thirty years of G-stability’ BIT 46 (2006), 479–489. |

[137] BUTCHER, J. C. ‘General linear methods’ Acta Numerica 15 (2006), 157–256. |

[136] BUTCHER, J. C., HILL, A.T. ‘Linear multistep methods as irreducible general linear methods’ BIT 46 (2006), 5–19. |

[135] BUTCHER, J. C., PODHAISKY, H. ‘On error estimation in general linear methods for stiff ODEs’ Appl. Numer. Math. 56 (2006), 345–357. |

[134] BUTCHER, J. C., WRIGHT, W.M. ‘Applications of doubly companion matrices’ Appl. Numer. Math. 56 (2006), 358–373. |

[133] BUTCHER, J. C. ‘High Order A-stable Numerical Methods for Stiff Problems’ Journal of Scientific Computing 25 (2005), 51–66. |

[132] BUTCHER, J. C., HOJJATI, G. ‘Second derivative methods with RK stability’ Numer. Algorithms 40 (2005), 415–429. |

[131] BUTCHER, J. C., RATTENBURY, N. ‘ARK Methods for Stiff Problems’ Appl. Numer. Math. 53 (2005), 165–181. |

[130] BUTCHER, J. C., JACKIEWICZ, Z. ‘Unconditionally Stable General Linear Methods for Ordinary Differential Equations’ BIT 44 (2004), 557–570. |

[129] BUTCHER, J. C., JACKIEWICZ, Z. ‘Construction of general linear methods with Runge-Kutta stability properties’ Numer. Algorithms 36 (2004), 53–72. |

[128] BUTCHER, J. C., ‘Some numerical methods for stiff problems’, In International Conference on Computational Methods in Science and Engineering, Kastoria, Greece, 12–16 September (2003), 93–97. |

[127] BUTCHER, J. C., WRIGHT, W.M. ‘The construction of practical general linear methods’ BIT 43 (2003), 695–721. |

[126] BUTCHER, J. C., ’Numerical Methods for Ordinary Differential Equations’, J. Wiley, Chichester, (2003), 435pp. |

[125] BUTCHER, J. C., MOIR ‘Experiments with a new fifth method’ Numer. Algorithms 33 (2003), 137–151. |

[124] BUTCHER, J. C., JACKIEWICZ, Z. ‘A new approach to error estimation for general linear methods’ Appl. Numer. Math. 95 (2003), 487–502. |

[123] BUTCHER, J. C., WRIGHT, W.M. ‘A transformation relating explicit and diagonally-implicit general linear methods’ Appl. Numer. Math. 44 (2003), 313–327. |

[122] BUTCHER, J. C. ‘Software issues for ordinary differential equations’ Numer. Algorithms 31 (2002), 401–418. |

[121] BUTCHER, J. C., CHAN, T.M.H. ‘A new approach to the algebraic structures for integration methods’ BIT 42 (2002), 477–489. |

[120] BUTCHER, J. C., O’SULLIVAN, A.E. ‘Nordsieck methods with an off-step point ’ Numer. Algorithms 31 (2002), 87–101. |

[119] BUTCHER, J. C., JACKIEWICZ, Z. ‘Error estimation for Nordsieck methods’ Numer. Algorithms 31 (2002), 75–85. |

[118] BUTCHER, J. C., HEARD, A.D. ‘Stability of numerical methods for ordinary differential equations’ Numer. Algorithms 31 (2002), 59–73. |

[117] BUTCHER, J. C. ‘The A-Stability of methods with Padé and generalized Padé stability functions’ Numer. Algorithms 31 (2002), 47–58. |

[116] BUTCHER, J. C., JACKIEWICZ, Z. ‘A reliable error estimation for diagonally implicit multistage integration methods’ BIT 41 (2001), 656–665. |

[115] BUTCHER, J. C., CHEN,D.J.L. ‘On the implementation of ESIRK methods for stiff IVPs’ Numer. Algorithms 26 (2001), 201–218. |

[114] BUTCHER, J. C., CHAN, T.M.H. ‘Variable stepsize schemes for effective order methods and enhanced order composition methods’ Numer. Algorithms 26 (2001), 131–150. |

[113] BUTCHER, J. C. ‘General linear methods for stiff differential equations’ BIT 41 (2001), 240–264. |

[112] BUTCHER, J. C.‘Numerical methods for ordinary differential equations in the 20th century’, In C. Brezinski and L. Wuytack (eds) Numerical Analysis: Historical Developments in the 20th Century North-Holland, Amsterdam, (2001), 449–478. |

[111] BUTCHER, J. C. ‘Numerical methods for ordinary differential equations in the 20th century’ J. Comput. Appl. Math. 125 (2000), 1-29. |

[110] BUTCHER, J. C., CHEN, D.J.L. ‘A new type of singly-implicit Runge-Kutta method’ Appl. Numer. Math. 34 (2000), 179-188. |

[109] BUTCHER, J. C., CHAN, T.M.H. ‘Multi-step zero approximations for stepsize control’ Appl. Numer. Math. 34 (2000), 167-177. |

[108] BUTCHER, J. C., SINGH, A.D. ‘The choice of parameters in parallel general linear methods for stiff problems’ Appl. Numer. Math. 34 (2000), 59-84. |

[107] BUTCHER, J. C., CHARTIER, P. , JACKIEWICZ, Z. ‘Experiments with a variable-order type 1 DIMSIM code’ Numerical Algorithms 22 (1999), 237-261. |

[106] IRWIN, R.J. HAUTUS, M.J., BUTCHER, J. C. ‘An area theorem for the same-different experiment’ Perception & Psychophysics 61(4) (1999), 766-769. |

[105] BUTCHER, J. C., CHARTIER, P. ‘The effective order of singly-implicit Runge-Kutta methods’ Numer. Algorithms 20 (1999), 269-284. |

[104] BUTCHER, J. C., CHEN, D.J.L. ‘ESIRK methods and variable stepsize’ Appl. Numer. Math. 28 (1998), 193-207. |

[103] BUTCHER, J. C. ‘Order and effective order’ Appl. Numer. Math. 28 (1998), 179-191. |

[102] BUTCHER, J. C. ‘ARK methods up to order five’ Numer. Algorithms 17 (1998), 193-221. |

[101] BUTCHER, J. C., DIAMANTAKIS, M.T. ‘DESIRE: diagonally extended singly implicit Runge-Kutta effective order methods’ Numer. Algorithms 17 (1998), 121-145. |

[100] BUTCHER, J. C., CHAN, R.P,K. ‘Efficient Runge-Kutta integrators for index-2 differential algebraic equations’ Math. Comp. 67 (1998), 1001-1021. |

[99] BUTCHER, J. C., JACKIEWICZ, Z. ‘Construction of high order diagonally implicit multistage integration methods for ordinary differential equations’ Appl. Numer. Math. 27 (1998), 1-12. |

[98] BUTCHER, J. C. ‘Numerical methods for differential equations and applications’ The Arabian Journal for Science and Engineering 22 #2C (1997), 17-29. |

[97] BUTCHER, J. C., CHARTIER, P., JACKIEWICZ, Z. ‘Nordsieck representation of DIMSIMs’ Numerical Algorithms 16 (1997), 209-230. |

[96] BUTCHER, J. C., JACKIEWICZ, Z. ‘Implementation of diagonally implicit multistage integration methods for ordinary differential equations’ SIAM J. Numer. Anal. 34 (1997), 2119-2141. |

[95] JACKIEWICZ, Z., MITTLEMAN, H.D.. ‘A nonlinear optimization approach to the construction of general linear methods of high order’ J. Comput. Appl. Math 81 (1997), 181-196. |

[94] BUTCHER, J. C. ‘An introduction to “Almost Runge-Kutta” methods’ Applied Numerical Mathematics 24 (1997), 331-342. |

[93] BUTCHER, J. C., TRACOGNA, S.. ‘Order conditions for two-step Runge-Kutta methods’ Applied Numerical Mathematics 24 (1997), 351-364. |

[92] BUTCHER, J. C., CHARTIER, P. . ‘A generalization of singly-implicit Runge-Kutta methods’ Applied Numerical Mathematics 24 (1997), 343-350. |

[91] BUTCHER, J. C. ‘Order and stabilityof parallel methods for stiff problems’ Advances in Computational Mathematics 7 (1997), 79-96. |

[90] BUTCHER, J. C., SANZ-SERNA, J.M.. ‘The number of conditions for a Runge-Kutta method to have effective order p’ Applied Numerical Mathematics 22 (1996), 103-111. |

[89] BUTCHER, J. C., WANNER, G.. ‘Runge-Kutta methods: some historical notes’ Applied Numerical Mathematics 22 (1996), 113-151. |

[88] BUTCHER, J. C., CASH, J.R.., DIAMANTAKIS, M.T.. ‘DESI methods for stiff initial value problems’ ACM Trans. Math. Software 22 (1996), 401-422. |

[87] BUTCHER, J. C., JACKIEWICZ, Z. ‘Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations’ Applied Numerical Mathematics 21 (1996), 385-415. |

[86] BUTCHER, J. C., ‘Runge-Kutta methods as mathematical objects”, In D. F. Griffiths and G. A. Watson (eds), Numerical Analysis: A. R. Mitchell 75th Birthday Volume, World Scientific Publishing Company, Singapore, (1996), 39-56. |

[85] BUTCHER, J. C. ‘A history of Runge-Kutta methods’ Applied Numerical Mathematics 20 (1996), 247-260. |

[84] BUTCHER, J. C. ‘General linear methods’ Comput. Math. Appl. 31 (1996), 105-112. |

[83] BUTCHER, J. C., ’Orthogonal polynomials, Pade approximations and A-stability’, Numerical Algorithms, 11 (1996), 71-78. |

[82] BUTCHER, J. C., CHARTIER, P.. ‘Parallel general linear methods for stiff ordinary differential and differential algebraic equations’ Applied Numerical Mathematics 17 (1995), 213-222. |

[81] BUTCHER, J. C. ‘On fifth order Runge-Kutta methods’ BIT 35 (1995), 202-209. |

[80] BUTCHER, J. C., CASH, J.R.., MOORE, G.., RUSSELL, R.D.. ‘Defect correction for two-point boundary value problems on non equidistant meshes’ Math Comp. 64 (1995), 629-648. |

[79] BUTCHER, J. C. ‘An introduction to DIMSIMs’ Comp. Appl. Math. 14 (1995), 59- 72. |

[78] BUTCHER, J. C., ‘Laguerre polynomials: applications in numerical ordinary differential equations’, In D. Brown et al (eds), Proceedings of the Cornelius Lanczos International Centenary Conference Society of Industrial and Applied Mathematics, Philadelphia, PA, (1994). 371-373. |

[77] BUTCHER, J. C. ‘Runge-Kutta methods in modern computation Part II: Implicit Runge-Kutta methods and related applications’ Computers in Physics 8 (1994), 512 - 517. |

[76] BUTCHER, J. C. ‘Runge-Kutta methods in modern computation Part I: Fundamental concepts’ Computers in Physics 8 (1994), 411 - 415. |

[75] BUTCHER, J. C. ‘Initial value problems: numerical methods and mathematics’ Computers and Mathematics with Applications 28 (1994), 1-16. |

[74] BUTCHER, J. C. ‘Some orbital test problems’ Computing 53 (1994), 75 - 94. |

[73] BUTCHER, J. C. ‘A transformation for the analysis of DIMSIMs’ BIT 34 (1994), 25 - 32. |

[72] BUTCHER, J. C., ‘The parallel solution of ordinary differential equations and some special functions’, In R.V.M. Zahar, (ed), Approximation and Computation, ISNM, 119, Birkhaeuser Verlag, Basel-Boston-Berlin, (1994), 67-76. |

[71] BUTCHER, J. C. ‘General linear methods for the parallel solution of ordinary differential equations’ World Sci. Ser. Appl. Anal. 2 (1993), 99-111. |

[70] BUTCHER, J. C., JACKIEWICZ, Z. ‘Diagonally implicit multistage integration methods for ordinary differential equations’ BIT 33 (1993), 452-472. |

[69] BUTCHER, J. C. ‘Diagonally-implicit multi-stage integration methods’ Appl. Numer. Math. 11 (1993), 347-363. |

[68] BUTCHER, J. C., JOHNSTON B.P., ’Estimating local truncation errors for Runge-Kutta methods’, J. Comput. and Applied Math., 45 (1993), special issue on Numerical Methods for Ordinary Differential Equations, Guest Editors: J. C. Butcher, J. R. Cash and P. J. van der Houwen, 203-212. |

[67] BUTCHER, J. C. ‘The role of orthogonal polynomials in numerical ordinary differential equations’ Journal of Computational and Applied Mathematics 43 (1992), 231-242. |

[66] BUTCHER, J. C., ‘Some new hybrid methods for initial value problems’, In J. R. Cash and I. Gladwell (eds), Computational Ordinary Differential Equations, Clarendon Press, Oxford, (1992), 29-46. |

[65] BUTCHER, J. C., CHIPMAN, F. H.. ‘Generalized Padé approximations to the exponential function’ BIT 32 (1992), 118-130. |

[64] BUTCHER, J. C. ‘The adaptation of STRIDE to delay differential equations’ Applied Numerical Mathematics 9 (1992), 415-425. |

[63] BUTCHER, J. C., CHAN, R.P,K. ‘On symmetrizers for Gauss methods’ Numerische Mathematik 60 (1992), 465-476. |

[62] BUTCHER, J. C., ‘The Fibonacci sequence, chromatic numbers and slam bidding’, Bull. IMA, (1990). |

[61] BUTCHER, J. C., ’Order, stepsize and stiffness switching’. Computing, 44, (1990), 209-220. |

[60] BUTCHER, J. C., CASH, J.R.. ‘Towards efficient Runge-Kutta methods for stiff systems’ SIAM J. Numer. Anal. 27 (1990), 753-761. |

[59] BUTCHER, J. C., CASH, J.R.., ’Some recent developments on numerical initial value problems: a survey’, Appl. Numer. Math., 5 (1989), special issue on Recent Theoretical Results in Numerical Ordinary Differential Equations, Guest Editor: J. C. Butcher, 3-18. |

[58] BUTCHER, J. C. ‘Towards efficient implementation of singly-implicit methods’ ACM Transactions Math. Software 14 (1988), 68-75. |

[57] BUTCHER, J. C. ‘On a class of matrices with real eigenvalues’ Linear Algebra Applns. 103 (1988), 1-12. |

[56] BUTCHER, J. C. ‘The equivalence of algebraic stability and AN-stability’ BIT 27 (1987), 510-533. |

[55] BUTCHER, J. C. ‘Linear and non-linear stability for general linear methods’ BIT 27 (1987), 182-189. |

[54] BUTCHER, J. C., ’The numerical analysis of ordinary differential equations: Runge- Kutta and general linear methods’, J. Wiley, Chichester, (1987), 512pp. |

[53] RABINOWITZ, P.J.R.., KAUTSKY, J.J.R.., ELHAY, S.J.R.., BUTCHER, J. C., ’On sequences of imbedded integration rules’, In ‘Numerical interpretation’, NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., 203 (1987), 113-139. |

[52] BUTCHER, J. C. ‘Optimal order and stepsize sequences’ IMA J. Numer. Anal. 6 (1986), 433-438. |

[51] BUTCHER, J. C. ‘The non-existence of ten stage eighth order explicit Runge-Kutta methods’ BIT 25 (1985), 521-540. |

[50] BUTCHER, J. C. ‘General linear methods: a survey’ Appl. Numer. Math. 1 (1985), 273-284. |

[49] BUTCHER, J. C. ‘An application of the Runge-Kutta space’ BIT 24 (1984), 425-440. |

[48] BUTCHER, J. C., COOPER, G.J. ‘An iterative scheme for implicit Runge-Kutta methods’ IMA J. Numer. Anal. 3 (1983), 127-140. |

[47] BUTCHER, J. C. ‘A short proof concerning B-stability’ BIT 22 (1982), 528-529. |

[46] BUTCHER, J. C. ‘A generalization of singly-implicit methods’ BIT 21 (1981), 175-189. |

[45] BUTCHER, J. C. ‘Stability properties for a general class of methods for ordinary differential equation’ SIAM J. Numer. Anal. 18 (1981), 37-44. |

[44] BUTCHER, J. C. ‘Some implementation schemes for implicit Runge-Kutta methods’ Lecture Notes in Mathematics 773 (1980), 12-24. |

[43] BURRAGE, K., BUTCHER, J. C., CHIPMAN, F. ‘Non-linear stability of a general class of differential equation methods’ BIT 20 (1980), 185-203. |

[42] BURRAGE, K., BUTCHER, J. C., CHIPMAN, F. ‘An implementation of singly-implicit Runge-Kutta methods’ BIT 20 (1980), 326-340. |

[41] BURRAGE, K., BUTCHER,J. C. ‘Stability criteria for implicit Runge-Kutta methods’ SIAM J. Numer. Anal. 16 (1979), 46-57. |

[40] BUTCHER, J. C. ‘A transformed implicit Runge-Kutta method’ J. Assoc. Comput. Mach. 26 (1979), 731-738. |

[39] BUTCHER, J. C. ‘On a conjecture concerning a set of sequences satisfying the Fibonacci difference equation’ Fibonacci Quarterly 16 (1976), 81- 83. |

[38] BUTCHER, J. C. ‘On A-stable Runge-Kutta methods’ BIT 17 (1977), 375-378. |

[37] 1976 BUTCHER, J. C.‘Runge-Kutta methods’ (Chapter 5) and ‘Implicit Runge-Kutta and related methods’(Chapter 10), in Modern numerical methods for ordinary differential equations (ed. G. Hall and J.M. Watt). |

[36] BUTCHER, J. C. ‘A class of implicit methods for ordinary differential equations’ Lecture notes in Mathematics 506 (1976), 28-37. |

[35] BUTCHER, J. C. ‘On the implementation of implicit Runge-Kutta methods’ BIT 16 (1976), 237-240. |

[34] BUTCHER, J. C. ‘A stability property of implicit Runge-Kutta methods’ BIT 15 (1975), 358-361. |

[33] BUTCHER, J. C. ‘An order bound for Runge-Kutta methods’ SIAM J. Numer. Anal. 12 (1975), 304-315. |

[32] BUTCHER, J. C. ‘Computation and theory in ordinary differential equations’ Math. Chronicle 3 (1974), 63-69. |

[31] BUTCHER, J. C. ‘Order conditions for general linear methods for ordinary differential equations’ ISNM 19 (1974), 77-81. |

[30] BUTCHER, J. C. ‘The order of differential equation methods’ Lecture Notes in Mathematics 362 (1974), 72-75. |

[29] BUTCHER, J. C., ‘Order conditions for a general class of numerical methods for ordinary differential equations’, in Topics in Numerical Analysis (ed. J.J.H. Miller), (1973), 35-40. |

[28] BUTCHER, J. C. ‘The order of numerical methods for ordinary differential equations’ Math. Comp. 27 (1973), 793-806. |

[27] BUTCHER, J. C. ‘A convergence criterion for a class of integration methods’ Math. Comp. 26 (1972), 107-117. |

[26] BUTCHER, J. C. ‘An algebraic theory of integration methods’ Math. Comp. 26 (1972), 79-106. |

[25] BUTCHER, J. C., ‘An approximation theorem in numerical analysis’, in A spectrum of Mathematics, (ed J. C. Butcher), Auckland and Oxford Univ. Presses, (1971), 121-125. |

[24] BUTCHER, J. C. ‘The effective order of Runge-Kutta methods’ Lecture Notes in Mathematics 109 (1969), 133-139. |

[23] BUTCHER, J. C. ‘A multistep generalization of Runge-Kutta methods with four or five stages’ J. Assoc. Comput. Mach. 14 (1967), 84-89. |

[22] BARKER, J. S. F., BUTCHER, J. C. ‘A simulation study of quasi-fixations of genes due to random fluctuation of selection intensities’ Genetics 53 (1966), 261-268. |

[21] BUTCHER, J. C. ‘On the convergence of numerical solutions of ordinary differential equations’ Math. Comp. 20 (1966), 1-10. |

[20] BUTCHER, J. C. ‘On the attainable order of Runge-Kutta methods’ Math. Comp. 19 (1965), 408-417. |

[19] BUTCHER, J. C., ’Some recent developments in the theory of Runge-Kutta methods’, Proceedings of I.F.I.P. Congress (New York) (1965),Vol.II. |

[18] BUTCHER, J. C. ‘A modified multistep method for the numerical integration of ordinary differential equations’ J. Assoc. Comput. Mach. 12 (1965), 124-135. |

[17] BUTCHER, J. C. ‘On Runge-Kutta processes of high order’ J. Austral. Math. Soc. 4 (1964), 179-194. |

[16] BUTCHER, J. C. ‘Integration processes based on Radau quadrature formulas’ Math. Comp. 18 (1964), 233-244. |

[15] BUTCHER, J. C. ‘Implicit Runge-Kutta processes’ Math. Comp. 18 (1964), 50-64. |

[14] BUTCHER, J. C. ‘On the integration processes of A. Huta’ J. Austral. Math. Soc. 3 (1963), 202-206. |

[13] BUTCHER, J. C. ‘Coefficients for the study of Runge-Kutta integration processes’ J. Austral. Math. Soc. 3 (1963), 185-201. |

[12] BUTCHER, J. C., Crawford, D.F., Messel, H., Smirnov, A.D., Varfolomeev, A.A. ‘Results on the angular and radial distributions of particles in electron-photon showers’ J. Phys. Soc. Japan 17 (1962), Suppl. A-III. |

[11] BUTCHER, J. C. ‘Random sampling from the normal distribution’ Computer J. 3 (1961), 251-253. |

[10] BUTCHER, J. C. ‘A partition test for pseudo-random numbers’ Math. Comp. 15 (1961), 198-199. |

[9] BUTCHER, J. C., Messel, H., ’Comparison of the electron number distribution in electron-photon showers in air and aluminium absorbers’, International Union of Pure and Applied Physics, (1960), p.243. |

[8] BOLT, B. A., BUTCHER, J. C. ‘Rayleigh wave dispersion for a single layer on an elastic half-space’ Australian J. of Physics 13 (1960), 498-504. |

[7] MESSEL, H, SMIRNOV, A. D., VARFOLOMEEV, A. A., CRAWFORD, D. F., BUTCHER, J. C. ‘Radial and angular distributions of electrons in electron-photon showers in lead and in emulsion absorbers’ Nuclear Physics 39 (1962), 1-88. |

[6] SRINIVASAN, S. K., BUTCHER, J. C., CHARTRES, B. A., MESSEL, H ‘Numerical calculations on the new approach to the cascade theory- III’ II Nuovo Cimento 9 (1958), 77-84. |

[5] BUTCHER, J. C., MESSEL, H ‘Electron number distribution in electron - photon Showers in Air and Aluminum Absorbers’ Nuclear Physics 20 (1960), 15-128. |

[4] BUTCHER, J. C., MESSEL, H ‘Electron number distribution in electron-photon Showers’ Physical Review 112 (1958), 2096-2106. |

[3] BUTCHER, J. C., CHARTRES, B. A., MESSEL, H ‘Tables of average numbers for electron - photon showers at small depths of absorber’ Nuclear Physics 6 (1958), 271-281. |

[2] BUTCHER, J. C., ‘On the numerical inversion of Laplace and Mellin transforms’, Proceedings of Computing Conference, Salisbury, S. Australia, (1957). |

[1] BUTCHER, J. C. ‘Treatment variances for experimental designs with serially correlated observations’ Biometrika 43 (1956), 208-212. |