#20040 Overall Influence

British mathematician

Arieh Iserles is a computational mathematician, currently Professor of the Numerical Analysis of Differential Equations at the University of Cambridge and a member of the Department of Applied Mathematics and Theoretical Physics.

Source: Wikipedia- Lie-group methods
- Efficient quadrature of highly oscillatory integrals using derivatives
- On the generalized pantograph functional-differential equation
- On the solution of linear differential equations in Lie groups
- On polynomials orthogonal with respect to certain Sobolev inner products
- On Quadrature Methods for Highly Oscillatory Integrals and Their Implementation
- A First Course in the Numerical Analysis of Differential Equations
- On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
- Arbitrary-Order Trigonometric Fourier Collocation Methods for Multi-Frequency Oscillatory Systems
- Stability of the discretized pantograph differential equation
- Geometric integration: numerical solution of differential equations on manifolds
- Generalized Leapfrog Methods
- On the Theory of Parallel Runge—Kutta Methods
- Approximating the exponential from a Lie algebra to a Lie group
- Stability and Dynamics of Numerical Methods for Nonlinear Ordinary Differential Equations
- On Neutral Functional–Differential Equations with Proportional Delays
- The optimal accuracy of difference schemes
- Numerical solution of isospectral flows
- The Pantograph Equation in the Complex Plane
- On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
- A Unified Approach to Spurious Solutions Introduced by Time Discretisation. Part I: Basic Theory
- Explicit Magnus expansions for nonlinear equations
- From high oscillation to rapid approximation I: modified Fourier expansions
- Geometric Numerical Integration
- Solving linear ordinary differential equations by exponentials of iterated commutators
- Quadrature methods for multivariate highly oscillatory integrals using derivatives
- Order Stars
- Effective Approximation for the Semiclassical Schrödinger Equation
- Exact and discretized stability of the pantograph equation
- On Pantograph Integro-Differential Equations
- On Cayley-Transform Methods for the Discretization of Lie-Group Equations
- Think globally, act locally: Solving highly-oscillatory ordinary differential equations
- Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions
- Reconstruction algorithm for single photon emission computed tomography and its numerical implementation
- Stability and Asymptotic Stability of Functional-Differential Equations
- Preserving algebraic invariants with Runge–Kutta methods
- Equilibria of Runge-Kutta methods
- A fast and simple algorithm for the computation of Legendre coefficients
- On the Method of Neumann Series for Highly Oscillatory Equations
- On the dynamics of a discretized neutral equation
- B-SERIES METHODS CANNOT BE VOLUME-PRESERVING
- Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations
- On highly oscillatory problems arising in electronic engineering
- On the A-Acceptability of Rational Approximations that Interpolate the Exponential Function
- On the theory of biorthogonal polynomials
- On the computation of highly oscillatory multivariate integrals with stationary points
- Runge-Kutta methods for orthogonal and isospectral flows
- Order Stars and a Saturation Theorem for First-order Hyperbolics
- Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential
- Highly Oscillatory Quadrature: The Story so Far
- Zeros of expansions in orthogonal polynomials
- On second-order differential equations with highly oscillatory forcing terms
- Time symmetry and high-order Magnus methods
- From high oscillation to rapid approximation III: multivariate expansions
- On transformations and zeros of polynomials
- Asymptotic expansion and quadrature of composite highly oscillatory integrals
- The spectral problem for a class of highly oscillatory Fredholm integral operators
- The asymptotic behaviour of certain difference equations with proportional delays
- Embedding of Delay Equations into an Infinite-Dimensional ODE System
- Explicit adaptive symplectic integrators for solving Hamiltonian systems
- On orthogonal polynomials transformed by the QR algorithm
- Unified approach to spurious solutions introduced by time discretization Part II: BDF-like methods
- On an Isospectral Lie–Poisson System and Its Lie Algebra
- On nonlinear delay differential equations
- Quadrature methods for stiff ordinary differential systems
- The computation of the spectra of highly oscillatory Fredholm integral operators
- On systems of differential equations with extrinsic oscillation
- Integro-differential Equations and Generalized Hypergeometric Functions
- Order stars and rational approximants to exp(z)
- Zeros of Transformed Polynomials
- On the Generalized Padé Approximations to the Exponential Function
- Barriers to Stability
- Runge-Kutta methods for quadratic ordinary differential equations
- Spectral theory of large Wiener–Hopf operators with complex-symmetric kernels and rational symbols
- Composite exponential approximations
- On numerical methods for highly oscillatory problems in circuit simulation
- Magnus--Lanczos Methods with Simplified Commutators for the Schrödinger Equation with a Time-Dependent Potential
- A Class of Integrable Flows on the Space of Symmetric Matrices
- Approximately preserving symmetries in the numerical integration of ordinary differential equations
- Stability and Accuracy of Semi-discretized Finite Difference Methods
- Rational Interpolation to $\exp ( - x)$ with Application to Certain Stiff Systems
- Composite Methods for Numerical Solution of Stiff Systems of ODE’s
- Computing Highly Oscillatory Integrals
- Runge–Kutta Methods for Neutral Differential Equations
- Orthogonality and approximation in a Sobolev space
- On the Discretization of Double-Bracket Flows
- From high oscillation to rapid approximation IV: accelerating convergence
- On skew-symmetric differentiation matrices
- COMMUTATORS OF SKEW-SYMMETRIC MATRICES
- A proof of the first dahlquist barrier by order stars
- Asymptotic solvers for oscillatory systems of differential equations
- Numerical Stability in the Presence of Variable Coefficients
- Bi-orthogonality and zeros of transformed polynomials
- Bi-orthogonality in rational approximation
- Christoffel-Darboux-type formulae and a recurrence for biorthogonal polynomials
- A note on Padé approximations and generalized hypergeometric functions
- Bi-orthogonal polynomials
- Generalized order star theory
- Numerical solution of Sturm–Liouville problems via Fer streamers
- Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials
- Two-step methods and bi-orthogonality
- Order Stars, Approximations and Finite Differences I. The General Theory of Order Stars
- Order Stars, Approximations and Finite Differences. III Finite Differences for $u_t = \omega u_{xx} $
- RUNGE–KUTTA METHODS ON MANIFOLDS
- Global Bounds on Numerical Error for Ordinary Differential Equations
- Numerical Methods on (and off) Manifolds
- On theA-stability of implicit Runge-Kutta processes
- Editorial
- Compact schemes for laser–matter interaction in Schrödinger equation based on effective splittings of Magnus expansion
- Efficient computation of delay differential equations with highly oscillatory terms
- Complex Dynamics of Convergence Acceleration
- From high oscillation to rapid approximation II: expansions in Birkhoff series
- On theA-Acceptability of Padé Approximations
- On the optimality of double-bracket flows
- Numerical recipes in C—the art of scientific computing, by W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling. Pp 735. £27·50. 1988. ISBN 0-521-35465-X (Cambridge University Press)
- Approximation by spline functions, by G. Nürnberger Pp 243. DM74. 1989. ISBN 3-540- 51618-2 (Springer)
- First-order Trace Formulae for the Iterates of the Fox–Li Operator
- Two-step numerical methods for parabolic differential equations
- The Joy and Pain of Skew Symmetry
- Orthogonal Systems with a Skew-Symmetric Differentiation Matrix
- On the Foundations of Computational Mathematics
- Magnus expansions and beyond
- Multistep methods on manifolds
- From high oscillation to rapid approximation V: the equilateral triangle
- Differential equations with general highly oscillatory forcing terms
- On Rapid Computation of Expansions in Ultraspherical Polynomials
- Dirichlet series for dynamical systems of first-order ordinary differential equations
- Complexity Theory for Lie-Group Solvers
- Nonlinear Stability and Asymptotics of O.D.E. Solvers
- The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory
- Error control of rational approximations to the exponential function
- Bi-orthogonality and zeros of transformed polynomials
- Parallel Computational Fluid Dynamics: Implementation and Results. Edited by H. D. SIMON. The MIT Press, 1992. 345 pp. £40.50.
- Applications of Magnus expansions and pseudospectra to Markov processes
- On the numerical analysis of rapid oscillation
- From orthogonal polynomials on the unit circle to functional equations via generating functions
- On zeros of Hankel determinants with iterated polynomial entries
- Order Stars, Approximations and Finite Differences II. Theorems in Approximation Theory
- Rational Approximations to the Exponential Function with Two Complex Conjugate Interpolation Points
- Error analysis of the extended Filon-type method for highly oscillatory integrals
- Why Geometric Numerical Integration?
- An Adaptive Filon Algorithm for Highly Oscillatory Integrals
- Explicit representations of biorthogonal polynomials
- A Family of Orthogonal Rational Functions and Other Orthogonal Systems with a skew-Hermitian Differentiation Matrix
- Asymptotic solvers for second-order differential equation systems with multiple frequencies
- On expansions in orthogonal polynomials
- A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals
- Asymptotic solvers for ordinary differential equations with multiple frequencies
- A-acceptability of derivatives of rational approximations to EXP(Z)
- Rational approximants and numerical methods for initial-value problems
- Convergence acceleration as a dynamical system
- Bi-orthogonality in rational approximation
- A constructive approach to the Schröder equation
- A-acceptable exponentially fitted combinations of three Padé approximations
- Spectral computation of highly oscillatory integral equations in laser theory
- Stiff equations
- Numerical analysis in Lie groups
- Aspects of generalized double-bracket flows
- Multistep Discretization of Linear Hyperbolic Equations
- A First Course in the Numerical Analysis of Differential Equations
- On Multivalued Exponential Approximations
- Chapter 7: Numerical Methods for Elliptic Problems
- Functional Fitting--New Family of Schemes for Integration of Stiff O.D.E.
- A-Stability and Dominating Pairs
- Biorthogonality and Its Applications to Numerical Analysis.
- Numerical mathematics, by G. Hämmerlin and K.-H. Hoffmann. Pp 422. DM74. 1991. ISBN 3-540-97494-6 (Springer)
- Matrix computations (2nd edition), by G. H. Golub and C. F. Van Loan. Pp 642. £38. 1989. ISBN 0-8018-3772-3 (John Hopkins Press)
- On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs
- Solving the wave equation with multifrequency oscillations
- Fast Computation of Orthogonal Systems with a Skew‐Symmetric Differentiation Matrix
- On a Curious q-Hypergeometric Identity
- From Schrödinger Spectra to Orthogonal Polynomials Via a Functional Equation
- Introduction
- Open problems
- General Order Stars
- Rational Approximants to the Exponential
- A-acceptability barriers
- Multistep methods
- The advection equation
- The diffusion equation
- Padé approximants
- Contractive approximation
- Numerical Analysis
- Biorthogonal polynomials: Recent developments
- Order stars, contractivity and a pick-type theorem
- Order stars and the structure of Padé tableaux
- Foreword
- Efficient Two-Step Numerical Methods for Parabolic Differential Equations
- Biorthogonal polynomials and zero-mapping transformations
- Preface to the second edition
- Preface to the first edition
- Flowchart of contents
- Euler's method and beyond
- Multistep methods
- Runge–Kutta methods
- Geometric numerical integration
- Error control
- Nonlinear algebraic systems
- Finite difference schemes
- The finite element method
- Spectral methods
- Gaussian elimination for sparse linear equations
- Classical iterative methods for sparse linear equations
- Multigrid techniques
- Conjugate gradients
- Fast Poisson solvers
- The diffusion equation
- Hyperbolic equations
- Bluffer's guide to useful mathematics
- Preface
- Computational methods in Viscous Aerodynamics. Edited by T. K. S. Murthy and C. A. BREBBIA. Elsevier, 1990. 370 pp. $133.25 or Dfl. 260.
- Computational Fluid Dynamics Review 1995. Edited by M. Hafez & K. Oshima. Wiley, 1995. 932 pp. ISBN 0-471-95589-2. £125.
- Numerical solution of differential equations (2nd edition), by M. K. Jain. Pp 698. £17·95. 1984. ISBN 0-85226-432-1 (Wiley Eastern)
- A complex beauty
- Simulation technique for RF oscillators
- Simulation of memristors in presence of high-frequency forcing function
- Banded, skew-symmetric differentiation matrices of high order
- Functional fitting–new family of schemes for integration of stiff O.D.E
- $A$-stability and dominating pairs
- Frequency fitting of rational approximations to the exponential functions
- Change of Editorship
- Dedication
- Banded, stable, skew-symmetric differentiation matrices of high order
- Editorial: Why Transactions of Mathematics and its Applications?
- Michael J. D. Powell. 29 July 1936—19 April 2015
- Time-domain modelling of interconnects with highly oscillatory sources
- Simulation of nonlinear systems subject to modulated chirp signals
- Optimality of double bracket and generalized double bracket flows
- On the Dimension of Certain Graded Lie Algebras Arising in Geometric Integration of Differential Equations
- On the Spectra of Certain Matrices Generated by Involutory Automorphisms
- COMMUTATORS OF SKEW-SYMMETRIC MATRICES
- EFFICIENT RUNGE–KUTTA METHODS FOR HAMILTONIAN EQUATIONS
- Order Stars
- Simulation of bimolecular reactions: Numerical challenges with the graph Laplacian
- Frequency Fitting of Rational Approximations to the Exponential Function
- The State of the Art in Numerical Analysis.
- Numerical Hamiltonian Problems.
- Numerical solution of partial differential equations: finite difference methods (3rd edition), by G. D. Smith. Pp 337. £20·00 (hardback), £10·95 (paperback). 1985. ISBN 0-19-859641-3/859650-2 (Oxford University Press)
- Numerical Solution of Differential Equations
- Elliptic differential equations: theory and numerical treatment, by W. Hackbusch. Pp 311 DM128. 1992. ISBN 3-540-54822-y (Springer)
- Nonlinear ordinary differential equations (2nd edition), by D. W. Jordan and P. Smith. Pp 381. £14·50 (paperback), £27·50 (hardback). 1987. ISBN 0-19-859657-X (Oxford University Press)
- Mathematics for large scale computing, edited by J. C. Diaz. Pp 368. $102. 1989. ISBN 0-8247-8122-8 (Marcel Dekker)
- Computing the Schrodinger equation with no fear of commutators
- Geometric Numerical Integration
- Optimal acceleration of convergence

Hebrew University of Jerusalem

Israeli university in Jerusalem

University of Cambridge

Collegiate public research university in Cambridge, England, United Kingdom

Ben-Gurion University of the Negev

Israeli University in Beersheba

Centre for Mathematical Sciences

Indian research institution devoted to mathematics and other related disciplines like statistics, theoretical physics, computer and information sciences

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