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 Gustaf Söderlind

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Average citations per article7.50
Citation Count150
Publication count20
Publication years1986-2011
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Average downloads per article902.00
Downloads (cumulative)902
Downloads (12 Months)28
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20 results found Export Results: bibtexendnoteacmrefcsv

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1
January 2011 Numerical Algorithms: Volume 56 Issue 1, January 2011
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 1

Grid adaptation in two-point boundary value problems is usually based on mapping a uniform auxiliary grid to the desired nonuniform grid. Here we combine this approach with a new control system for constructing a grid density function � ( x ). The local mesh width Δ x j �+�1/2 �=� ...
Keywords: Singular problems, Singularly perturbed problems, Boundary value problems, Grid generation, Grid refinement, Error equidistribution, Ordinary differential equations, Step size control, Adaptivity

2
June 2008 Journal of Complexity: Volume 24 Issue 3, June, 2008
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 2

In this paper we analyze the problem of adaptivity for one-step numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating grids of minimal computational cost for which the local error is below a prescribed tolerance (optimal grids). The grids are generated by introducing an auxiliary ...
Keywords: Adaptive step size control, Adaptive numerical methods, Boundary value problems, Hölder mean, Information-based complexity, Ordinary differential equations, Initial value problems

3
August 2007 Journal of Computational and Applied Mathematics: Volume 205 Issue 2, August, 2007
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 4

In linear multistep methods with variable step size, the method's coefficients are functions of the step size ratios. The coefficients therefore need to be recomputed on every step to retain the method's proper order of convergence. An alternative approach is to use step density control to make the method adaptive. ...
Keywords: Multistep method, Variable step size method, Non-uniform grid, Step size selection, Step density control, 65L05

4
March 2006 Applied Numerical Mathematics: Volume 56 Issue 3-4, March, 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 4

The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and ...
Keywords: Signal processing, Step size selection, Control, Reversible systems, Adaptivity

5
March 2006 Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ: Volume 56 Issue 3, March 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 3

The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and ...
Keywords: reversible systems, adaptivity, signal processing, control, step size selection

6
January 2006 Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics: Volume 185 Issue 2, 15 January 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 2

Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have ...
Keywords: Algorithm analysis, Mathematical software, ODE software, 65L05-Numerical analysis, Adaptive time-stepping, Computational stability, Software, Work/precision, Ordinary differential equations-initial value problems, Software testing, DAE software, Test protocols

7
January 2006 Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics: Volume 185 Issue 2, 15 January 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 5

We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of DASSL and a modified version, ...
Keywords: 65L05-Numerical Analysis, Algorithm analysis, Digital filters, Mathematical software, Adaptive time-stepping, Computational stability, Multistep methods, Ordinary Differential Equations-initial value problems, DASSL, PI control, Stepsize control

8
January 2006 Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics: Volume 185 Issue 2, 15 January 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 2

We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of DASSL and a modified version, ...
Keywords: computational stability, digital filters, algorithm analysis, mathematical software, adaptive time-stepping, stepsize control, DASSL, PI control

9
January 2006 Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics: Volume 185 Issue 2, 15 January 2006
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 1

Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have ...
Keywords: ODE software, algorithm analysis, mathematical software, test protocols, work/precision, adaptive time-stepping, software testing, DAE software, computational stability

10
June 2005 SIAM Journal on Scientific Computing: Volume 26 Issue 6, 2005
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 8

Adaptive step size control is difficult to combine with geometric numerical integration. As classical step size control is based on "past" information only, time symmetry is destroyed and with it the qualitative properties of the method. In this paper we develop completely explicit, reversible, symmetry-preserving, adaptive step size selection algorithms ...
Keywords: explicit and reversible step size control, reversible perturbation theory, Hamiltonian systems, geometric integration, Störmer--Verlet method, backward error analysis, Adaptive integration, time reversible and symmetric methods

11 published by ACM
March 2003 ACM Transactions on Mathematical Software (TOMS): Volume 29 Issue 1, March 2003
Publisher: ACM
Bibliometrics:
Citation Count: 23
Downloads (6 Weeks): 1,   Downloads (12 Months): 28,   Downloads (Overall): 902

Full text available: PDFPDF
Adaptive time-stepping based on linear digital control theory has several advantages: the algorithms can be analyzed in terms of stability and adaptivity, and they can be designed to produce smoother stepsize sequences resulting in significantly improved regularity and computational stability. Here, we extend this approach by viewing the closed-loop transfer ...
Keywords: digital filters, Adaptivity, algorithm analysis, mathematical software, control theory, stepsize control, error control

12
December 2000 Applied Numerical Mathematics: Volume 35 Issue 4, Dec., 2000
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 3

Keywords: half-explicit methods, difference corrected multistep methods, differential algebraic equations (DAE), multistep methods, partitioned methods, β-blocked methods

13
December 1998 SIAM Journal on Scientific Computing: Volume 20 Issue 1, Aug. 1998
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 9

The prediction of stage values in implicit Runge--Kutta methods is important both for overall efficiency as well as for the design of suitable control strategies for the method. The purpose of this paper is to construct good stage value predictors for implicit methods and to verify their behavior in practical ...
Keywords: implicit Runge--Kutta, control strategies, convergence, Newton iteration, predictors

14
December 1997 Journal of Computational and Applied Mathematics: Volume 86 Issue 2, Dec. 10, 1997
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 10

Keywords: error analysis, ordinary differential equations, Runge-Kutta methods, error bounds

15
January 1997 SIAM Journal on Scientific Computing: Volume 18 Issue 1, January. 1997
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 17

In the numerical solution of ODEs by implicit time-stepping methods, a system of (nonlinear) equations has to be solved each step. It is common practice to use fixed-point iterations or, in the stiff case, some modified Newton iteration. The convergence rate of such methods depends on the stepsize. Similarly, a ...
Keywords: numerical solution of ODEs, stepsize control, iterative solution of nonlinear equations, control strategies

16
May 1993 SIAM Journal on Scientific Computing: Volume 14 Issue 3, May 1993
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 19

Keywords: dummy derivative, constraint stabilization, solution invariant, index reduction, automatic differentiation, differential-algebraic

17 published by ACM
May 1989 Proceedings of the conference on Numerical ordinary differential equations
Publisher: ACM
Bibliometrics:
Citation Count: 0


18
May 1989 Applied Mathematics and Computation: Volume 31, May, 1989
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

In this paper we describe the development of an experimental multi-purpose integration system. Strongly modular, the system allows the use of wide classes of multistep methods for solving ODE's, singulsr perturbation problems as well as implicit differential-algebraic equations. We focus our attention on a new family of collocation methods for ...

19
February 1988 BIT: Volume 28 Issue 2, February 1988
Publisher: BIT Computer Science and Numerical Mathematics
Bibliometrics:
Citation Count: 30


20
November 1986 Numerische Mathematik: Volume 50 Issue 1, 1986
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 5




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