Adrian Hill

Dr

  • 4 WEST 1.14

20022019
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Research Output 2002 2019

2019

Error estimates for semi-Lagrangian finite difference methods applied to Burgers' equation in one dimension

Cook, S., Budd, C., Hill, A. & Melvin, T., 21 Jun 2019, In : Applied Numerical Mathematics. 145, p. 261-282 22 p.

Research output: Contribution to journalArticle

2016
5 Citations (Scopus)
64 Downloads (Pure)

Symmetric general linear methods

Butcher, J. C., Hill, A. T. & Norton, T. J. T., 1 Dec 2016, In : BIT Numerical Mathematics. 56, 4, p. 1189-1212 24 p.

Research output: Contribution to journalArticle

Open Access
File
General Linear Methods
Runge Kutta methods
Differential equations
Symmetry
One-step Method
2015
1 Citation (Scopus)
24 Downloads (Pure)

An iterative starting method to control parasitism for the Leapfrog method

Hill, A. & Norton, T., 1 Jan 2015, In : Applied Numerical Mathematics. 87, 1, p. 145 156 p., Volume 87.

Research output: Contribution to journalArticle

File
Hamiltonians
Iteration
Computational Results
Euler equations
Time Scales
2014
14 Citations (Scopus)
53 Downloads (Pure)

The control of parasitism in $G$-symplectic methods

Butcher, J. C., Habib, Y., Hill, A. T. & Norton, T. J. T., 14 Oct 2014, In : SIAM Journal on Numerical Analysis (SINUM). 52, 5, p. 2440-2465 26 p.

Research output: Contribution to journalArticle

Open Access
File
Symplectic Methods
Hamiltonians
General Linear Methods
Cancel
Small Perturbations
2011
10 Citations (Scopus)

Exponential stability of time-varying linear systems

Hill, A. T. & Ilchmann, A., Jul 2011, In : IMA Journal of Numerical Analysis. 31, 3, p. 865-885 21 p.

Research output: Contribution to journalArticle

Linear Time-varying Systems
Exponential Stability
Asymptotic stability
Linear systems
Stability Estimates
2010
8 Citations (Scopus)

Algebraically stable diagonally implicit general linear methods

Hewitt, L. L. & Hill, A. T., Jun 2010, In : Applied Numerical Mathematics. 60, 6, p. 629-636 8 p.

Research output: Contribution to journalArticle

General Linear Methods
Implicit Method
Differential equations
Stiff Differential Equations
Series
5 Citations (Scopus)

G-matrices for algebraically stable general linear methods

Hill, A. T., 1 Mar 2010, In : Numerical Algorithms. 53, 2-3, p. 281-292 12 p.

Research output: Contribution to journalArticle

Generalized Eigenproblem
General Linear Methods
Eigenvalues and eigenfunctions
Eigenvector

Nonautonomous stability of linear multistep methods

Boutelje, B. R. & Hill, A. T., Apr 2010, In : IMA Journal of Numerical Analysis. 30, 2, p. 525-542 18 p.

Research output: Contribution to journalArticle

Linear multistep Methods
Initial value problems
Initial Value Problem
Scalar
Lipschitz Function
2009
13 Citations (Scopus)

Algebraically stable general linear methods and the G-matrix

Hewitt, L. L. & Hill, A. T., Mar 2009, In : BIT Numerical Mathematics. 49, 1, p. 93-111 19 p.

Research output: Contribution to journalArticle

General Linear Methods
Algebraic Riccati Equation
Riccati equations
Order Conditions
Reformulation
3 Citations (Scopus)
Rotating
Approximation
One-leg Methods
Unstable
Linear multistep Methods
2007
3 Citations (Scopus)

The Z-transform and linear multistep stability

Coughlan, J. J., Hill, A. T. & Logemann, H., 2007, In : IMA Journal of Numerical Analysis. 27, 1, p. 45-73 29 p.

Research output: Contribution to journalArticle

2006
14 Citations (Scopus)

Linear multistep methods as irreducible general linear methods

Butcher, J. C. & Hill, A. T., 2006, In : BIT Numerical Mathematics. 46, 1, p. 5-19 15 p.

Research output: Contribution to journalArticle

14 Citations (Scopus)

Nonlinear stability of general linear methods

Hill, A. T., 2006, In : Numerische Mathematik. 103, 4, p. 611-629 19 p.

Research output: Contribution to journalArticle

2005

Multistep approximation of linear sectorial evolution equations

Hill, A. T., 2005, In : IMA Journal of Numerical Analysis. 25, 1, p. 45-56 12 p.

Research output: Contribution to journalArticle

2004

Analysis and numerics for a parabolic equation with impulsive forcing

Hill, A. T. & Wan, W. L., 2004, In : Applied Numerical Mathematics. 50, 3-4, p. 445-474 30 p.

Research output: Contribution to journalArticle

2002
2 Citations (Scopus)

On a multistep method approximating a linear sectorial evolution equation

Del Buono, N. & Hill, A. T., 2002, In : IMA Journal of Numerical Analysis. 22, 3, p. 481-499 19 p.

Research output: Contribution to journalArticle