Publications: Refereed Journals

  1. Jing Gao & Arieh Iserles, "A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals", BIT (2017), DOI 10.1007/s10543-017-0682-9.
  2. Jing Gao & Arieh Iserles, "Error analysis of the extended Filon-type method for highly oscillatory integrals", to appear in Research in the Mathematical Sciences (2017).
  3. E. Hairer & A. Iserles, "Banded, stable, skew-symmetric differentiation matrices of high order", IMA J. Num. Anal. 37 (2017), 1087–1103.
  4. P. Bader, A. Iserles, K. Kropielnicka & P. Singh, "Efficient methods for time-dependence in semiclassical Schrödinger equations" , Proc. Royal Soc. A (2016) DOI: 10.1098/rspa.2015.0733.
  5. A. Iserles, "The joy and pain of skew-symmetry", Found. Comp. Maths 16, 1607–1630 (2016).
  6. E. Hairer & A. Iserles, "Numerical stability in the presence of variable coefficients" Found. Comp. Maths 16 (2016), 751–777.
  7. M. Condon, J. Gao & A. Iserles, "Asymptotic solvers for highly oscillatory semi-explicit DAEs" Discr. & Cont. Dyn. Sys. A 36 (2016), 4813–4837.
  8. M. J. Cantero & A. Iserles, "From orthogonal polynomials on the unit circle to functional equations via generating functions" Transactions Amer. Maths Soc. 368 (2016), 4027–4063.
  9. Bin Wang, Arieh Iserles & Xinyuan Wu, "Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems", Found. Comp. Maths 16 (2016), 151–181.
  10. A.G.C. P. Ramos & A. Iserles, "Numerical solution of Sturm–Liouville problems via Fer streamers" Numerische Mathematik 131 (2015), 541–565.
  11. M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for ordinary differential equations with multiple frequencies", Sci. China Maths 58 (2015), 2279–2300.
  12. P. Bader, A. Iserles, K. Kropielnicka & P. Singh, "Effective approximation for the linear time-dependent Schrödinger equation", Found. Comp. Maths 14 (2014), 689–720.
  13. B. Wang & A. Iserles, "Dirichlet series for dynamical systems of first-order ordinary differential equations", Disc. & Cont. Dynamical Sys. B 19 (2014), 281–298.
  14. M. Condon, A. Iserles & S.P. Nørsett, "Differential equations with general highly oscillatory forcing terms" , Proc. Royal Soc. A 470 (2014), 20130490.
  15. S. Altinbasak Üsküplu, M. Condon, A. Deaño &A. Iserles, "Highly oscillatory diffusion-type equations", J. Comp. Maths. 31 (2014), 549–572.
  16. A. Iserles, "On skew-symmetric differentiation matrices", IMA J. Num. Anal. 34 (2014), 435–451.
  17. M. J. Cantero & A. Iserles, "On expansions in orthogonal polynomials", Adv. Comp. Maths 38 (2013), 35–61.
  18. M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for second-order differential equation systems with multiple frequencies" Calcolo 51 (2014), 109–139.
  19. S. Blanes & A. Iserles, "Explicit adaptive symplectic integrators for solving Hamiltonian systems" Celestial Mech. & Dynamical Astronomy 114 (2012) 297–317.
  20. A. Condon, A. Deaño & A. Iserles, "Simulation of memristors in presence of high-frequency forcing function", Electromic Letters 48 (2012), 684–686.
  21. M. Condon, A. Deaño, A. Iserles & K. Kropielnicka, "Efficient computation of delay differential equations with highly oscillatory terms" M2AN 46 (2012), 1407–1420.
  22. A. Boettcher, S. Grudsky, D. Huybrechs & A. Iserles, "First-order trace formulas for the iterates of the Fox–Li operator" Operator Theory: Advances and Applications 218 (2012) 207–224.
  23. M. J. Cantero & A. Iserles, "On rapid computation of expansions in ultraspherical polynomials" SIAM J. Num. Anal. 50 (2012), 307–327.
  24. B. Adcock, A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation II: Expansions in Birkhoff series", IMA J. Num. Anal. 32 (2012), 105–140.
  25. M. Condon, A. Deaño & A. Iserles, "A new simulation technique for RF oscillators", Electronics Letters (2011) 47 13.
  26. H. Brunner, A. Iserles & S. Nørsett, "The computation of the spectra of highly oscillatory Fredholm integral operators", J. Integral Eqns & Applcs 23 (2011), 467–519.
  27. D. Huybrechs, A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation IV: Accelerating convergence", IMA J. Num. Anal. 31 (2011), 442–468.
  28. D. Huybrechs, A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation V: The equilateral triangle", IMA J. Num. Anal. 31 (2011), 755–785.
  29. A. Boettcher, S. Grudsky & A. Iserles, "Spectral theory of large Wiener–Hopf operators with complex-symmetric kernels and rational symbols", Math. Proceedings Cambridge Phil. Soc. 151 (2011), 161–191.
  30. A. Iserles, "A fast and simple algorithm for the computation of Legendre coefficients", Numerische Mathematik 117 (2011), 529–553.
  31. A. Boettcher, H. Brunner, A. Iserles & S.P. Nørsett, "On the singular values and eigenvalues of the Fox–Li and related operators", New York J. Maths 16 (2010), 539–561.
  32. A. Iserles & D. Levin, "Asymptotic expansion and quadrature of composite highly oscillatory integrals", Maths Comp 80 (2011), 279–296.
  33. M. Condon, A. Deaño & A. Iserles, "On second order differential equations with highly oscillatory forcing terms", Proc. Royal Soc. A 466 (2010), 1809–1828.
  34. M. Condon, A. A. Deaño & A. Iserles, "On systems of differential equations with extrinsic oscillation", Discr. & Cont. Dynamical Sys. 28 (2010), 1345–1367.
  35. H. Brunner, A. Iserles & S.P. Nørsett, "The spectral problem for a class of highly oscillatory Fredholm differential equations" IMA J. Num. Anal. 30 (2010), 108–130.
  36. M. Condon, A. Deaño, A. Iserles, K. Maczynski & T. Xu, "On numerical methods for highly oscillatory problems in circuit simulation", COMPEL 28 (2009), 1607–1618.
  37. A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation III: Multivariate expansions", IMA J. Num. Anal. 29 (2009), 882–916.
  38. M. Condon, A. Deaño & A. Iserles,"On highly oscillatory problems arising in electronic engineering", M2AN 43 (2009), 785–804.
  39. A.M. Bloch, V. Brizanescu, A. Iserles, J.E. Marsden & T.S. Ratiu, "A class of integrable geodesic flows on the symplectic group and the symmetric matrices", Comm. Math. Phys. 290 (2009), 399–435.
  40. A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation I: Modified Fourier expansions", IMA J. Num. Anal. 28 (2008), 862–887.
  41. A. Iserles, G.R.W. Quispel & P.S.P. Tse, "B-series methods cannot be volume preserving", BIT 47 (2007), 351–378.
  42. A. Iserles & S.P. Nørsett, "On the computation of highly oscillatory multivariate integrals with critical points", BIT 46 (2006), 549–566.
  43. A. Iserles & S.P. Nørsett, "Quadrature methods for multivariate highly oscillatory integrals using derivatives", Maths Comp 75 (2006), 1233–1258.
  44. F. Casas & A. Iserles, "Explicit Magnus expansions for nonlinear equations", J. Phys. A: Math. Gen 39 (2006), 5445–5461.
  45. A.M. Bloch & A. Iserles, "On an isospectral Lie–Poisson system and its Lie algebra", Found. Comp. Maths 6 (2006), 121–144.
  46. A.S. Fokas, A. Iserles & V. Marinakis, "Reconstruction algorithms for positron emission tomography and single photon emission computed tomography and their numerical implementation", J. Royal Soc. Interface 3 (2006), 45–54.
  47. A. Iserles & A. Zanna, "Efficient computation of the matrix exponential by generalized polar decompositions", SIAM J. Num. Anal. 42 (2005), 2218–2256.
  48. A. Iserles & S.P. Nørsett, "Efficient quadrature of highly oscillatory integrals using derivatives", Proc. Royal Soc. A 461 (2005), 1383–1399.
  49. A.M. Bloch & A. Iserles, "Commutators of skew-symmetric matrices'', Intl J. Bif. & Chaos 15 (2005), 793–801.
  50. A. Iserles, "On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators", IMA J. Num. Anal. 25 (2005), 25–44.
  51. A. Iserles & S.P. Nørsett, "On quadrature methods for highly oscillatory integrals and their implementation", BIT 44 (2004), 755–772.
  52. A.M. Bloch & A. Iserles,"On the optimality of double-bracket flows", Intl J. Maths & Mathematical Sc. 62 (2004), 3301–3319.
  53. A. Iserles, "On the method of Neumann series for highly oscillatory equations"BIT 44 (2004), 473–488.
  54. A. Iserles & A. Zanna, "On the spectra of certain matrices generated by involutory automorphisms", SIAM J. Matrix Anal. 22 (2004), 1110–1123.
  55. A. Iserles, "On the numerical quadrature of highly-oscillating integrals I: Fourier transforms'', IMA J. Num. Anal. 24 (2004), 365–391.
  56. A. Iserles, "On the global error of discretization methods for highly-oscillatory ordinary differential equations'', BIT 42 (2002), 561–599.
  57. A. Iserles,"Think globally, act locally: solving highly-oscillatory ordinary differential equations'', Appld Num. Anal. 43 (2002), 145–160.
  58. A. Iserles, "On the discretization of double-bracket flows'', Found. Comp. Maths 2 (2002), 305–329.
  59. E. Celledoni, A. Iserles, S.P. Nørsett & B. Orel, "Complexity theory for Lie-group solvers'', J. Complexity 18 (2002), 242–286.
  60. A. Iserles & X. Liu, "Optimal acceleration of convergence'', Math. Analysis & Applics 8 (2001), 15–32.
  61. A. Iserles, S.P. Nørsett & A.F. Rasmussen, "Time-symmetry and high-order Magnus methods'', Appld Num. Maths 39 (2001), 379–401.
  62. M.P. Calvo, A. Iserles & A. Zanna, "Semi-explicit methods for isospectral flows'', Adv. Comp. Maths 14 (2001), 1–24.
  63. A. Iserles, "On Cayley-transform methods for the discretization of Lie-group equations'', Found. Comp. Maths b>1 (2001), 129–160.
  64. E. Celledoni & A. Iserles, "Methods for the approximation of the matrix exponential in a Lie-algebraic setting'', IMA J. Num. Anal. 21 (2001), 463–488.
  65. A. Iserles, "Multistep methods on manifolds'', IMA J. Num. Anal. 21 (2001), 407–419.
  66. A. Iserles, "A Magnus expansion for the equation Y'=AY-YB'', J. Comp. Maths 19 (2001), 15–26.
  67. A. Iserles & A. Zanna, "Preserving algebraic invariants with Runge–Kutta methods'', J. Comp. Appl. Maths 125 (2000), 69–81.
  68. A. Iserles, "How large is the exponential of a banded matrix?'', J. New Zealand Maths Soc. 29 (2000), 177–192.
  69. E. Celledoni & A. Iserles, "Approximating the exponential from a Lie algebra to a Lie group'', Maths of Comp. 69 (2000), 1457–1480.
  70. A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett & A. Zanna, "Lie-group methods'', Acta Numerica 9 (2000), 215–365.
  71. A. Iserles & A. Zanna, "On the dimension of certain graded Lie algebras arising in geometric integration of differential equations'', LMS J. Comput. & Maths 3 (2000), 44–75.
  72. A. Iserles, R. McLachlan & A. Zanna, "Approximately preserving symmetries in numerical integration'', Europ. J. Appl. Maths 10 (1999), 419–445.
  73. M.P. Calvo, A. Iserles & A. Zanna, "Conservative methods for the Toda lattice equations'', IMA J. Num. Anal. 19 (1999), 509–523.
  74. A. Iserles, A. Marthinsen & S.P. Nørsett, "On the implementation of the method of Magnus series for linear differential equations'', BIT 39 (1999), 28–304.
  75. A. Iserles & S.P. Nørsett, "On the solution of linear differential equations on Lie groups'', Phil. Trans Royal Soc. A 357 (1999), 983–1019.
  76. A. Iserles, G.P. Ramaswami & M. Sofroniou, "Runge–Kutta methods for quadratic ordinary differential equations'', BIT 38 (1998), 315–346.
  77. A. Iserles, "Exact and discretized stability of the pantograph equation'', Appl. Num. Maths 24 (1997), 295–308.
  78. M.P. Calvo, A. Iserles & A. Zanna, "Numerical solution of isospectral flows'', Maths of Comp. 66 (1997), 1461–1486.
  79. G. Derfel & A. Iserles, "The pantograph equation in the complex plane'', J. Math. Anal. & Applcs 213 (1997), 117–132.
  80. A. Iserles & Y. Liu, "Integro-differential equations and generalized hypergeometric functions'', J. Math. Anal. & Applcs 208 (1997), 404–424.
  81. A. Iserles & Y. Liu, "On neutral functional-differential equations with proportional delays'', J. Math. Anal. & Applcs 207 (1997), 73–95.
  82. A. Iserles & S.P. Nørsett, "Biorthogonal polynomials and zero-mapping transformations'' ,Comp. & Maths Applcs 33 (1997), 129–143.
  83. B.J.C. Baxter & A. Iserles,"On approximation by exponentials'', Annals of Num. Maths 4 (1997), 39–54.
  84. M.P. Calvo, A. Iserles & A. Zanna, "Runge–Kutta methods for orthogonal and isospectral flows'', Appl. Num. Maths 22 (1996), 153–163.
  85. A. Iserles, "Biorthogonal polynomials: Recent developments'', Num. Algorithms 11 (1996), 215–228.
  86. A. Iserles & S.P. Nørsett, "Explicit representations of biorthogonal polynomials'', Num. Algorithms 10 (1995), 51–68.
  87. A. Iserles & J. Terjéki, "Stability and asymptotic stability of functional-differential equations'', J. London Math. Soc. 51 (1995), 559–572.
  88. A. Feldstein, A. Iserles & D. Levin, "Embedding of delay equations into an infinite-dimensional ODE system'', J. Diff. Eqns 117 (1995), 127–150.
  89. A. Iserles & S.P. Nørsett, "Biorthogonal polynomials in numerical ODEs'', Ann. Num. Maths 1 (1994), 153–170.
  90. A. Iserles & Y. Liu, "On pantograph integro-differential equations'', J. Integral Eqns & Appls 6 (1994), 213–237.
  91. A. Iserles, "Convergence acceleration as a dynamical system'', Appl. Num. Maths 15 (1994), 101–121.
  92. A. Iserles, "On nonlinear delay differential equations'', Trans. Amer. Math. Soc. 344 (1994), 441–477.
  93. A. Iserles, "Numerical analysis of delay differential equations with variable delays'', Ann. Num. Maths 1 (1994), 133–152.
  94. A. Iserles, "The asymptotic behaviour of certain difference equations with proportional delay'', Computers Maths Applic. 28 (1994), 141–152.
  95. M.D. Buhmann & A. Iserles, "Stability of the discretized pantograph differential equation'', Maths Comp. 60 (1993), 575–589.
  96. A. Iserles, "A constructive approach to the Schröder equation'', J. Comp. Appl. Maths 46 (1993), 301–314.
  97. A. Iserles & G. Söderlind, "Global bounds on numerical error for ordinary differential equations'', J. Complexity 9 (1993), 97–112. (Republished in Festschrift for Joseph F. Traub (H. Wozniakowski, ed.), Academic Press, New York (1993), 97–112.)
  98. A. Iserles, "On the generalized pantograph functional-differential equation'', Europ. J. Appl. Maths 4 (1993), 1–38.
  99. M.D. Buhmann & A. Iserles, "On orthogonal polynomials transformed by the QR algorithm'', J. Comp. Appl. Maths 43 (1992), 117–134.
  100. A. Iserles, "Rational approximants and numerical methods for initial-value problems'', Physica D 60 (1992), 280–292.
  101. A. Iserles & A.M. Stuart, "A unified approach to spurious solutions introduced by time discretization. Part II: BDF-like methods'', IMA J. Num. Anal. 12 (1992), 487–502.
  102. A. Iserles, E.B. Saff & Xiaoyan Liu, "On zeros of Hankel determinants with iterated polynomial entries'', IMA J. Num. Anal. 12 (1992), 387–403.
  103. M.D. Buhmann & A. Iserles, "On the dynamics of a discretized neutral equation'', IMA J. Num. Anal. 12 (1992), 339–363.
  104. A. Iserles, A.T. Peplow & A.M. Stuart, "A unified approach to spurious solutions introduced by time discretization. Part I: Basic theory'', SIAM J. Num. Anal. 28 (1991), 1723–1751.
  105. A. Iserles, S.P. Nørsett & E.B. Saff, "On transformations and zeros of polynomials'', Rocky Mntn J. Maths 21 (1991), 331–357.
  106. A. Iserles, P.E. Koch, S.P. Nørsett & J.M. Sanz-Serna, "On polynomials orthogonal with respect to certain Sobolev inner products'', J. Approx. Th. 65 (1991), 151–175.
  107. A. Iserles, "Efficient Runge–Kutta methods for Hamiltonian equations'', Bull. Hellenic Math. Soc. 32 (1991), 3–20. (Republished in Advances in Computer Mathematics and its Applications (E.A. Lipitakis, ed.), World Scientific, Singapore (1993), 107–124.)
  108. A. Iserles, "Complex dynamics of convergence acceleration'', IMA J. Num. Anal. 11 (1991), 205–240.
  109. E. Hairer, A. Iserles & J.M. Sanz-Serna, "Equilibria of Runge–Kutta methods'', Numer. Math. 58 (1990), 243–254.
  110. A. Iserles & S.P. Nørsett, "On the theory of parallel Runge–Kutta methods'', IMA J. Num. Anal. 10 (1990), 463–488.
  111. A. Iserles & S.P. Nørsett, "Zeros of transformed polynomials'', SIAM J. Math. Anal. 21 (1990), 483–509.
  112. A. Iserles, "Stability and dynamics of numerical methods for nonlinear ordinary differential equations'', IMA J. Num. Anal. 10 (1990), 1–30.
  113. A. Iserles & S.P. Nørsett, "Christoffel–Darboux-type formulae and a recurrence for bi-orthogonal polynomials'', J. Constr. Approx. 5 (1989), 437–453.
  114. A. Iserles & E.B. Saff, "Zeros of expansions in orthogonal polynomials'', Math. Proc. Camb. Phil. Soc. 105 (1989), 559–573.
  115. A. Iserles & S.P. Nørsett, "Order stars and rational approximants to exp(z)'', Appl. Num. Maths 5 (1989), 63–70.
  116. A. Iserles & S.P. Nørsett, "On the theory of bi-orthogonal polynomials'', Trans. Amer. Math. Soc. 306 (1988), 455–474.
  117. A. Iserles & S.P. Nørsett, "Two-step methods and bi-orthogonality'', Maths Comp. 49 (1987), 543–552.
  118. A. Iserles & E.B. Saff, "Bi-orthogonality in rational approximation'', J. Comp. & Appl. Maths 19 (1987), 47–54.
  119. A. Iserles & S.P. Nørsett, "Bi-orthogonality and zeros of transformed polynomials'', J. Comp. & Appl. Maths 19 (1987), 39–45.
  120. A. Iserles, "Generalized leapfrog methods'', IMA J. Num. Anal. 6 (1986), 381–392.
  121. A. Iserles & S.P. Nørsett, "Error control of rational approximations to the exponential function'', J. Constr. Approx. 2 (1986), 41–57.
  122. A. Iserles, "Multistep discretisation of linear hyperbolic equations'', IMA J. Num. Anal. 6 (1985), 293–307.
  123. E. Hairer, A. Iserles & S.P. Nørsett, ``Rational approximations to the exponential function with two complex conjugate interpolation points'', SIAM J. Math. Anal. 16 (1985), 814–821.
  124. A. Iserles, "Order stars, approximations and finite differences III. Finite differences for ut= uxx'', SIAM J. Math. Anal. 16 (1985), 1020–1033.
  125. A. Iserles, "Order stars, approximations and finite differences II. Theorems in approximation theory'', SIAM J. Math. Anal. 16 (1985), 785–802.
  126. A. Iserles, "Order stars, approximations and finite differences I. The general theory of order stars'', SIAM J. Math. Anal. 16 (1985), 559–576.
  127. A. Iserles & S.P. Nørsett, "A-acceptability of derivatives of rational approximations to exp(z)'', J. Approx. Th. 43 (1985), 327–337.
  128. A. Iserles & S.P. Nørsett, "A proof of the first Dahlquist barrier by order stars'', BIT 24 (1984), 529–537.
  129. A. Iserles & R.A. Renaut, "Stability and accuracy of semi-discretized finite difference methods'', IMA J. Num. Anal. 4 (1984), 289–307.
  130. A. Iserles, "Solving linear ordinary differential equations by exponentials of iterated commutators'', Numer. Math. 45 (1984), 183–199.
  131. A. Iserles, "Composite methods for numerical solution of stiff systems of O.D.E.'s'', SIAM J. Num. Anal. 21 (1984), 340–351.
  132. G. Strang & A. Iserles, "Barriers to stability'', SIAM J. Num. Anal. 20 (1983), 1251–1257.
  133. A. Iserles & G. Strang, "The optimal accuracy of difference schemes'', Trans. Amer. Math. Soc. 277 (1983), 779–803.
  134. A. Iserles & S.P. Nørsett, "Frequency fitting of rational approximations to the exponential function'', Maths Comp. 40 (1983), 547–559.
  135. A. Iserles, "Order stars and a saturation theorem for first order hyperbolics'', IMA J. Num. Anal. 2 (1982), 49–61.
  136. A. Iserles, "Composite exponential approximations'', Maths Comp. 38 (1982), 99–112.
  137. A. Iserles & M.J.D. Powell, "On the A-acceptability of rational approximations that interpolate the exponential function'', IMA J. Num. Anal. 1 (1981), 241–251.
  138. A. Iserles, "Two-step numerical methods for parabolic P.D.E.'s,'' BIT 21 (1981), 80–96.
  139. A. Iserles, "On multivalued exponential approximations'', SIAM J. Num. Anal. 18 (1981), 480–499.
  140. A. Iserles, "Quadrature methods for stiff ordinary differential systems'', Maths Comp. 36 (1981), 171–182.
  141. A. Iserles, "Rational interpolation to e-x with application to certain stiff systems'', SIAM J. Num. Anal. 18 (1981), 1–14.
  142. A. Iserles, "Nonexponential fitting techniques for numerical solution of stiff equations'', Utilitas Mathematica 17 (1980), 276–302.
  143. A. Iserles, "On the A-acceptability of Padé approximations'', SIAM J. Math. Anal. 10 (1979), 1002–1007.
  144. A. Iserles & G. Della Riccia, "PATREC: a computer program for automatic identification of patterns'', Pol. Anal. and Inf. Sys. 3 (1979), 91–100.
  145. A. Iserles, "A note on Padé approximations and generalized hypergeometric functions'', BIT 19 (1979), 573–575.
  146. A. Iserles, "On the generalized Padé approximations to the exponential function'', SIAM J. Num. Anal. 16 (1979), 631–636.
  147. A. Iserles, "On the A-stability of implicit Runge–Kutta processes'', BIT 18 (1978), 157–169.
  148. A. Iserles, "A-acceptable exponentially fitted combinations of three Padé approximations'', J. Comp. & Appl. Maths 4 (1978), 143–146.
  149. A. Iserles, "A-stability and dominating pairs'', Maths Comp. 32 (1978), 19–33.
  150. A. Iserles, "Functional fitting—new family of schemes for integration of stiff O.D.E.'', Maths Comp. 31 (1977), 112–123.