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Numerical algorithms, ISSN 1572-9265, 2019, Volume 81, Issue 4, pp. 1343 - 1359
For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two... 
Algorithms | Algebra | IMEX methods | Numerical Analysis | Computer Science | Numeric Computing | SSP property | DIMSIMs | Theory of Computation | Stability analysis | Construction of highly stable methods | General linear methods | MATHEMATICS, APPLIED | SYSTEMS | GENERAL MONOTONICITY | Analysis | Differential equations
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 05/2015, Volume 279, pp. 40 - 56
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 05/2020, Volume 151, pp. 282 - 300
We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of... 
Continuous extensions | Stability analysis | Local discretization errors | General linear methods | Stage order and order conditions | MATHEMATICS, APPLIED | ERROR ESTIMATION | CONSTRUCTION | IMPLEMENTATION | DIMSIMS | MULTISTAGE INTEGRATION METHODS
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 2018, Volume 343, pp. 174 - 188
In this paper we investigate the strong stability preserving (SSP) property of transformed diagonally implicit multistage integration methods (DIMSIMs). Within... 
Strong stability preserving | DIMSIMs | General linear methods | Monotonicity | Construction of methods | Transformed methods | MATHEMATICS, APPLIED | STEPSIZE RESTRICTIONS | SEARCH | RUNGE-KUTTA-METHODS | HIGH-ORDER | ALGEBRAICALLY STABLE 2-STEP | CONSTRUCTION | MULTISTAGE INTEGRATION METHODS | NORDSIECK METHODS
Journal Article
Mathematics and computers in simulation, ISSN 0378-4754, 2019, Volume 176, pp. 206 - 225
We consider the class of implicit–explicit (IMEX) general linear methods (GLMs) to construct methods where the explicit part has strong stability preserving... 
SSP property | Stability analysis | Inherent Runge–Kutta stability | Construction of highly stable methods | IMEX methods | General linear methods | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Inherent Runge-Kutta stability | CONSTRUCTION | MONOTONICITY | DIMSIMS
Journal Article
Mathematical Modelling and Analysis, ISSN 1392-6292, 04/2011, Volume 16, Issue 1, pp. 82 - 96
We derive suffcient conditions which guarantee that the stability polynomial of Nordsieck method for ordinary differential equations has only two nonzero... 
Nordsieck methods | inherent quadratic stability | order conditions | general linear methods | Inherentquadratic stability | Order conditions | General linear methods | MATHEMATICS | IMPLEMENTATION | DIMSIMS | ORDINARY DIFFERENTIAL-EQUATIONS | Stability | Computer simulation | Searching | Roots | Differential equations | Mathematical models | Modelling | Models
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 10/2017, Volume 120, pp. 165 - 175
We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q=p. Order conditions... 
Order conditions | Starting procedures | Generalized Runge–Kutta methods | General linear methods | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | STABILITY | CONSTRUCTION | IMPLEMENTATION | DIMSIMS | MULTISTAGE INTEGRATION METHODS | Generalized Runge-Kutta methods | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 11/2017, Volume 121, pp. 234 - 248
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 3, pp. A1430 - A1453
In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes... 
Implicit-explicit integration | General linear methods | Dimsim | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | MODEL | FLOW | implicit-explicit integration | RUNGE-KUTTA SCHEMES | ELEMENT | NAVIER-STOKES EQUATIONS | FORMULATIONS | general linear methods | DISCONTINUOUS GALERKIN METHODS | CONSTRUCTION | DIMSIM
Journal Article
Computational & applied mathematics, ISSN 2238-3603, 07/2020, Volume 39, Issue 3
We introduce a class of implicit-explicit (IMEX) schemes for the numerical solution of initial value problems of differential equations with both non-stiff and... 
MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | STABILITY | Second derivative methods | IMPLEMENTATION | Order conditions | Stability analysis | HIGH-ORDER | IMEX schemes | General linear methods | PEER METHODS | CONSTRUCTION | DIMSIMS | TYPE-1
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 2010, Volume 60, Issue 6, pp. 629 - 636
This paper concerns algebraically stable diagonally implicit general linear methods, intended for stiff differential equations. The first step in the... 
DIMSIMs | Stiff problems | Algebraic stability | General linear methods | MATHEMATICS, APPLIED | STABILITY | CONSTRUCTION | MULTISTAGE INTEGRATION METHODS | ORDINARY DIFFERENTIAL-EQUATIONS
Journal Article
Numerical Algorithms, ISSN 1017-1398, 2/1999, Volume 22, Issue 3, pp. 237 - 261
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 2006, Volume 56, Issue 3, pp. 533 - 543
Journal Article
Numerical Algorithms, ISSN 1017-1398, 5/2004, Volume 36, Issue 1, pp. 53 - 72
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 2002, Volume 42, Issue 1, pp. 251 - 267
Some issues related to the implementation of diagonally implicit multistage integration methods for stiff differential systems are discussed. They include... 
Nordsieck representation | DIMSIMs | Simplified Newton iterations | Local error estimation for stiff systems | MATHEMATICS, APPLIED | simplified Newton iterations | CONSTRUCTION | EQUATIONS | local error estimation for stiff systems | HIGH-ORDER | MULTISTAGE INTEGRATION METHODS | GENERAL LINEAR METHODS | TYPE-1
Journal Article
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