- Arieh Iserles & Shev Macnamara, "Magnus expansions and pseudospectra of master equations", to appear in
*Europ. J. Appld Maths*(2018). - Changying Liu, Arieh Iserles & Xinyuan Wu, "Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations",
*J. Comp. Phys.***356**, 1–30 (2018). - Marissa Condon & Arieh Iserles, "Time-domain modelling of interconnects with highly oscillatory sources",to appear in
*COMPEL*. - Jing Gao & Arieh Iserles, "A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals",
*BIT*(2017), DOI 10.1007/s10543-017-0682-9. - 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). - E. Hairer & A. Iserles, "Banded, stable, skew-symmetric differentiation matrices of high order",
*IMA J. Num. Anal.***37**(2017), 1087–1103. - 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. - A. Iserles, "The joy and pain of skew-symmetry",
*Found. Comp. Maths***16**, 1607–1630 (2016). - E. Hairer & A. Iserles, "Numerical stability in the presence of variable coefficients"
*Found. Comp. Maths***16**(2016), 751–777. - M. Condon, J. Gao & A. Iserles, "Asymptotic solvers for highly oscillatory semi-explicit DAEs"
*Discr. & Cont. Dyn. Sys. A***36**(2016), 4813–4837. - 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. - Bin Wang, Arieh Iserles & Xinyuan Wu, "Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems",
*Found. Comp. Maths***16**(2016), 151–181. - A.G.C. P. Ramos & A. Iserles, "Numerical solution of Sturm–Liouville problems via Fer streamers"
*Numerische Mathematik***131**(2015), 541–565. - M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for ordinary differential equations with multiple frequencies",
*Sci. China Maths***58**(2015), 2279–2300. - P. Bader, A. Iserles, K. Kropielnicka & P. Singh, "Effective approximation for the linear time-dependent Schrödinger equation",
*Found. Comp. Maths***14**(2014), 689–720. - B. Wang & A. Iserles, "Dirichlet series for dynamical systems of first-order ordinary differential equations",
*Disc. & Cont. Dynamical Sys. B***19**(2014), 281–298. - M. Condon, A. Iserles & S.P. Nørsett, "Differential equations with general highly oscillatory forcing terms" ,
*Proc. Royal Soc. A***470**(2014), 20130490. - S. Altinbasak Üsküplu, M. Condon, A. Deaño &A. Iserles, "Highly oscillatory diffusion-type equations",
*J. Comp. Maths*.**31**(2014), 549–572. - A. Iserles, "On skew-symmetric differentiation matrices",
*IMA J. Num. Anal.***34**(2014), 435–451. - M. J. Cantero & A. Iserles, "On expansions in orthogonal polynomials",
*Adv. Comp. Maths***38**(2013), 35–61. - M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for second-order differential equation systems with multiple frequencies"
*Calcolo***51**(2014), 109–139. - S. Blanes & A. Iserles, "Explicit adaptive symplectic integrators for solving Hamiltonian systems"
*Celestial Mech. & Dynamical Astronomy***114**(2012) 297–317. - A. Condon, A. Deaño & A. Iserles, "Simulation of memristors in presence of high-frequency forcing function",
*Electromic Letters***48**(2012), 684–686. - M. Condon, A. Deaño, A. Iserles & K. Kropielnicka, "Efficient computation of delay differential equations with highly oscillatory terms"
*M2AN***46**(2012), 1407–1420. - 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. - M. J. Cantero & A. Iserles, "On rapid computation of expansions in ultraspherical polynomials"
*SIAM J. Num. Anal.***50**(2012), 307–327. - 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. - M. Condon, A. Deaño & A. Iserles, "A new simulation technique for RF oscillators",
*Electronics Letters*(2011)**47**13. - 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. - D. Huybrechs, A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation IV: Accelerating convergence",
*IMA J. Num. Anal.***31**(2011), 442–468. - 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. - 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. - A. Iserles, "A fast and simple algorithm for the computation of Legendre coefficients",
*Numerische Mathematik***117**(2011), 529–553. - 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. - A. Iserles & D. Levin, "Asymptotic expansion and quadrature of composite highly oscillatory integrals",
*Maths Comp***80**(2011), 279–296. - M. Condon, A. Deaño & A. Iserles, "On second order differential equations with highly oscillatory forcing terms",
*Proc. Royal Soc. A***466**(2010), 1809–1828. - M. Condon, A. A. Deaño & A. Iserles, "On systems of differential equations with extrinsic oscillation"
*, Discr. & Cont. Dynamical Sys.***28**(2010), 1345–1367. - 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. - 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. - A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation III: Multivariate expansions",
*IMA J. Num. Anal.***29**(2009), 882–916. - M. Condon, A. Deaño & A. Iserles,"On highly oscillatory problems arising in electronic engineering",
*M2AN***43**(2009), 785–804. - 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. - A. Iserles & S.P. Nørsett, "From high oscillation to rapid approximation I: Modified Fourier expansions",
*IMA J. Num. Anal.***28**(2008), 862–887. - A. Iserles, G.R.W. Quispel & P.S.P. Tse, "B-series methods cannot be volume preserving",
*BIT***47**(2007), 351–378. - A. Iserles & S.P. Nørsett, "On the computation of highly oscillatory multivariate integrals with critical points",
*BIT***46**(2006), 549–566. - A. Iserles & S.P. Nørsett, "Quadrature methods for multivariate highly oscillatory integrals using derivatives",
*Maths Comp***75**(2006), 1233–1258. - F. Casas & A. Iserles, "Explicit Magnus expansions for nonlinear equations",
*J. Phys. A: Math. Gen***39**(2006), 5445–“5461. - A.M. Bloch & A. Iserles, "On an isospectral Lie–Poisson system and its Lie algebra",
*Found. Comp. Maths***6**(2006), 121–144. - 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. - A. Iserles & A. Zanna, "Efficient computation of the matrix exponential by generalized polar decompositions",
*SIAM J. Num. Anal.***42**(2005), 2218–2256. - A. Iserles & S.P. Nørsett, "Efficient quadrature of highly oscillatory integrals using derivatives",
*Proc. Royal Soc. A***461**(2005), 1383–1399. - A.M. Bloch & A. Iserles, "Commutators of skew-symmetric matrices'',
*Intl J. Bif. & Chaos***15**(2005), 793–801. - A. Iserles, "On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators",
*IMA J. Num. Anal.***25**(2005), 25–44. - A. Iserles & S.P. Nørsett, "On quadrature methods for highly oscillatory integrals and their implementation",
*BIT***44**(2004), 755–772. - A.M. Bloch & A. Iserles,"On the optimality of double-bracket flows",
*Intl J. Maths & Mathematical Sc.***62**(2004), 3301–3319. - A. Iserles, "On the method of Neumann series for highly oscillatory equations"
*BIT***44**(2004), 473–488. - A. Iserles & A. Zanna, "On the spectra of certain matrices generated by involutory automorphisms",
*SIAM J. Matrix Anal.***22**(2004), 1110–1123. - A. Iserles, "On the numerical quadrature of highly-oscillating integrals I: Fourier transforms'',
*IMA J. Num. Anal.***24**(2004), 365–391. - A. Iserles, "On the global error of discretization methods for highly-oscillatory ordinary differential equations'',
*BIT***42**(2002), 561–599. - A. Iserles,"Think globally, act locally: solving highly-oscillatory ordinary differential equations'',
*Appld Num. Anal.***43**(2002), 145–160. - A. Iserles, "On the discretization of double-bracket flows'',
*Found. Comp. Maths***2**(2002), 305–329. - E. Celledoni, A. Iserles, S.P. Nørsett & B. Orel, "Complexity theory for Lie-group solvers'',
*J. Complexity***18**(2002), 242–286. - A. Iserles & X. Liu, "Optimal acceleration of convergence'',
*Math. Analysis & Applics***8**(2001), 15–32. - A. Iserles, S.P. Nørsett & A.F. Rasmussen, "Time-symmetry and high-order Magnus methods'',
*Appld Num. Maths***39**(2001), 379–401. - M.P. Calvo, A. Iserles & A. Zanna, "Semi-explicit methods for isospectral flows'',
*Adv. Comp. Maths***14**(2001), 1–24. - A. Iserles, "On Cayley-transform methods for the discretization of Lie-group equations'',
*Found. Comp. Maths*b>1 (2001), 129–160. - 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. - A. Iserles, "Multistep methods on manifolds'',
*IMA J. Num. Anal.***21**(2001), 407–419. - A. Iserles, "A Magnus expansion for the equation
*Y'=AY-YB*'',*J. Comp. Maths***19**(2001), 15–26. - A. Iserles & A. Zanna, "Preserving algebraic invariants with Runge–Kutta methods'',
*J. Comp. Appl. Maths***125**(2000), 69–81. - A. Iserles, "How large is the exponential of a banded matrix?'',
*J. New Zealand Maths Soc.***29**(2000), 177–192. - E. Celledoni & A. Iserles, "Approximating the exponential from a Lie algebra to a Lie group'',
*Maths of Comp.***69**(2000), 1457–1480. - A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett & A. Zanna, "Lie-group methods'',
*Acta Numerica***9**(2000), 215–365. - 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. - A. Iserles, R. McLachlan & A. Zanna, "Approximately preserving symmetries in numerical integration'',
*Europ. J. Appl. Maths***10**(1999), 419–445. - M.P. Calvo, A. Iserles & A. Zanna, "Conservative methods for the Toda lattice equations'',
*IMA J. Num. Anal.***19**(1999), 509–523. - 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. - A. Iserles & S.P. Nørsett, "On the solution of linear differential equations on Lie groups'',
*Phil. Trans Royal Soc. A***357**(1999), 983–1019. - A. Iserles, G.P. Ramaswami & M. Sofroniou, "Runge–Kutta methods for quadratic ordinary differential equations'',
*BIT***38**(1998), 315–346. - A. Iserles, "Exact and discretized stability of the pantograph equation'',
*Appl. Num. Maths*24 (1997), 295–308. - M.P. Calvo, A. Iserles & A. Zanna, "Numerical solution of isospectral flows'',
*Maths of Comp.***66**(1997), 1461–1486. - G. Derfel & A. Iserles, "The pantograph equation in the complex plane'',
*J. Math. Anal. & Applcs***213**(1997), 117–132. - A. Iserles & Y. Liu, "Integro-differential equations and generalized hypergeometric functions'',
*J. Math. Anal. & Applcs***208**(1997), 404–424. - A. Iserles & Y. Liu, "On neutral functional-differential equations with proportional delays'',
*J. Math. Anal. & Applcs***207**(1997), 73–95. - A. Iserles & S.P. Nørsett, "Biorthogonal polynomials and zero-mapping transformations'' ,
*Comp. & Maths Applcs***33**(1997), 129–143. - B.J.C. Baxter & A. Iserles,"On approximation by exponentials'',
*Annals of Num. Maths***4**(1997), 39–54. - M.P. Calvo, A. Iserles & A. Zanna, "Runge–Kutta methods for orthogonal and isospectral flows'',
*Appl. Num. Maths***22**(1996), 153–163. - A. Iserles, "Biorthogonal polynomials: Recent developments'',
*Num. Algorithms***11 (1996), 215–228.** - A. Iserles & S.P. Nørsett, "Explicit representations of biorthogonal polynomials'',
*Num. Algorithms***10**(1995), 51–68. - A. Iserles & J. Terjéki, "Stability and asymptotic stability of functional-differential equations'',
*J. London Math. Soc.***51**(1995), 559–572. - A. Feldstein, A. Iserles & D. Levin, "Embedding of delay equations into an infinite-dimensional ODE system'',
*J. Diff. Eqns***117**(1995), 127–150. - A. Iserles & S.P. Nørsett, "Biorthogonal polynomials in numerical ODEs'',
*Ann. Num. Maths***1**(1994), 153–170. - A. Iserles & Y. Liu, "On pantograph integro-differential equations'',
*J. Integral Eqns & Appls***6**(1994), 213–237. - A. Iserles, "Convergence acceleration as a dynamical system'',
*Appl. Num. Maths***15**(1994), 101–121. - A. Iserles, "On nonlinear delay differential equations'',
*Trans. Amer. Math. Soc.***344**(1994), 441–477. - A. Iserles, "Numerical analysis of delay differential equations with variable delays'',
*Ann. Num. Maths***1**(1994), 133–152. - A. Iserles, "The asymptotic behaviour of certain difference equations with proportional delay'',
*Computers Maths Applic.***28**(1994), 141–152. - M.D. Buhmann & A. Iserles, "Stability of the discretized pantograph differential equation'',
*Maths Comp.***60**(1993), 575–589. - A. Iserles, "A constructive approach to the Schröder equation'',
*J. Comp. Appl. Maths***46**(1993), 301–314. - 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.) - A. Iserles, "On the generalized pantograph functional-differential equation'',
*Europ. J. Appl. Maths***4**(1993), 1–38. - M.D. Buhmann & A. Iserles, "On orthogonal polynomials transformed by the QR algorithm'',
*J. Comp. Appl. Maths***43**(1992), 117–134. - A. Iserles, "Rational approximants and numerical methods for initial-value problems'',
*Physica D***60**(1992), 280–292. - 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. - A. Iserles, E.B. Saff & Xiaoyan Liu, "On zeros of Hankel determinants with iterated polynomial entries'',
*IMA J. Num. Anal.***12**(1992), 387–403. - M.D. Buhmann & A. Iserles, "On the dynamics of a discretized neutral equation'',
*IMA J. Num. Anal.***12**(1992), 339–363. - 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. - A. Iserles, S.P. Nørsett & E.B. Saff, "On transformations and zeros of polynomials'',
*Rocky Mntn J. Maths***21**(1991), 331–357. - 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. - 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.) - A. Iserles, "Complex dynamics of convergence acceleration'',
*IMA J. Num. Anal.***11**(1991), 205–240. - E. Hairer, A. Iserles & J.M. Sanz-Serna, "Equilibria of Runge–Kutta methods'',
*Numer. Math.***58**(1990), 243–254. - A. Iserles & S.P. Nørsett, "On the theory of parallel Runge–Kutta methods'',
*IMA J. Num. Anal.***10**(1990), 463–488. - A. Iserles & S.P. Nørsett, "Zeros of transformed polynomials'',
*SIAM J. Math. Anal.***21**(1990), 483–509. - A. Iserles, "Stability and dynamics of numerical methods for nonlinear ordinary differential equations'',
*IMA J. Num. Anal.***10**(1990), 1–30. - A. Iserles & S.P. Nørsett, "Christoffel–Darboux-type formulae and a recurrence for bi-orthogonal polynomials'',
*J. Constr. Approx.***5**(1989), 437–453. - A. Iserles & E.B. Saff, "Zeros of expansions in orthogonal polynomials'',
*Math. Proc. Camb. Phil. Soc.***105**(1989), 559–573. - A. Iserles & S.P. Nørsett, "Order stars and rational approximants to exp
*(z)*'',*Appl. Num. Maths***5**(1989), 63–70. - A. Iserles & S.P. Nørsett, "On the theory of bi-orthogonal polynomials'',
*Trans. Amer. Math. Soc.***306**(1988), 455–474. - A. Iserles & S.P. Nørsett, "Two-step methods and bi-orthogonality'',
*Maths Comp.***49**(1987), 543–552. - A. Iserles & E.B. Saff, "Bi-orthogonality in rational approximation'',
*J. Comp. & Appl. Maths***19**(1987), 47–54. - A. Iserles & S.P. Nørsett, "Bi-orthogonality and zeros of transformed polynomials'',
*J. Comp. & Appl. Maths***19 (1987), 39–45.** - A. Iserles, "Generalized leapfrog methods'',
*IMA J. Num. Anal.***6**(1986), 381–392. - A. Iserles & S.P. Nørsett, "Error control of rational approximations to the exponential function'',
*J. Constr. Approx.***2**(1986), 41–57. - A. Iserles, "Multistep discretisation of linear hyperbolic equations'',
*IMA J. Num. Anal.***6**(1985), 293–307. - 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. - A. Iserles, "Order stars, approximations and finite differences III. Finite differences for
*u*'',_{t}= u_{xx}*SIAM J. Math. Anal.***16**(1985), 1020–1033. - A. Iserles, "Order stars, approximations and finite differences II. Theorems in approximation theory'',
*SIAM J. Math. Anal.***16**(1985), 785–802. - A. Iserles, "Order stars, approximations and finite differences I. The general theory of order stars'',
*SIAM J. Math. Anal.***16**(1985), 559–576. - A. Iserles & S.P. Nørsett, "A-acceptability of derivatives of rational approximations to exp
*(z)*'',*J. Approx. Th*.**43**(1985), 327–337. - A. Iserles & S.P. Nørsett, "A proof of the first Dahlquist barrier by order stars'',
*BIT***24**(1984), 529–537. - A. Iserles & R.A. Renaut, "Stability and accuracy of semi-discretized finite difference methods'',
*IMA J. Num. Anal.***4**(1984), 289–307. - A. Iserles, "Solving linear ordinary differential equations by exponentials of iterated commutators'',
*Numer. Math.***45**(1984), 183–199. - A. Iserles, "Composite methods for numerical solution of stiff systems of O.D.E.'s'',
*SIAM J. Num. Anal.***21**(1984), 340–351. - G. Strang & A. Iserles, "Barriers to stability'',
*SIAM J. Num. Anal.***20**(1983), 1251–1257. - A. Iserles & G. Strang, "The optimal accuracy of difference schemes'',
*Trans. Amer. Math. Soc.***277**(1983), 779–803. - A. Iserles & S.P. Nørsett, "Frequency fitting of rational approximations to the exponential function'',
*Maths Comp.***40**(1983), 547–559. - A. Iserles, "Order stars and a saturation theorem for first order hyperbolics'',
*IMA J. Num. Anal.***2**(1982), 49–61. - A. Iserles, "Composite exponential approximations'',
*Maths Comp.***38**(1982), 99–112. - 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. - A. Iserles, "Two-step numerical methods for parabolic P.D.E.'s,''
*BIT***21**(1981), 80–96. - A. Iserles, "On multivalued exponential approximations'',
*SIAM J. Num. Anal.***18**(1981), 480–499. - A. Iserles, "Quadrature methods for stiff ordinary differential systems'',
*Maths Comp.***36**(1981), 171–182. - A. Iserles, "Rational interpolation to e
with application to certain stiff systems'',^{-x}*SIAM J. Num. Anal.***18**(1981), 1–14. - A. Iserles, "Nonexponential fitting techniques for numerical solution of stiff equations'',
*Utilitas Mathematica***17**(1980), 276–302. - A. Iserles, "On the A-acceptability of Padé approximations'',
*SIAM J. Math. Anal.***10**(1979), 1002–1007. - A. Iserles & G. Della Riccia, "PATREC: a computer program for automatic identification of patterns'',
*Pol. Anal. and Inf. Sys.***3**(1979), 91–100. - A. Iserles, "A note on Padé approximations and generalized hypergeometric functions'',
*BIT***19**(1979), 573–575. - A. Iserles, "On the generalized Padé approximations to the exponential function'',
*SIAM J. Num. Anal.***16**(1979), 631–636. - A. Iserles, "On the A-stability of implicit Runge–Kutta processes'',
*BIT***18**(1978), 157–169. - A. Iserles, "A-acceptable exponentially fitted combinations of three Padé approximations'',
*J. Comp. & Appl. Maths***4**(1978), 143–146. - A. Iserles, "A-stability and dominating pairs'',
*Maths Comp.***32**(1978), 19–33. - A. Iserles, "Functional fitting—new family of schemes for integration of stiff O.D.E.'',
*Maths Comp.***31**(1977), 112–123.