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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
Journal of scientific computing, ISSN 1573-7691, 2019, Volume 80, Issue 2, pp. 784 - 807
In this paper strong stability preserving (SSP) properties of Runge-Kutta methods obtained by composing k different schemes with different step sizes are... 
65L05 | 65L06 | MATHEMATICS, APPLIED | Radius of absolute monotonicity | STEPSIZE RESTRICTIONS | Initial value problem | Strong stability preserving | ABSOLUTE MONOTONICITY | CONTRACTIVITY | SSP | NUMERICAL-SOLUTION | 65L20 | Runge-Kutta | Composition method | Monotonicity | 65M20
Journal Article
Mathematical Modelling and Analysis, ISSN 1392-6292, 09/2015, Volume 20, Issue 5, pp. 552 - 577
Journal Article
Mathematics of computation, ISSN 0025-5718, 7/1991, Volume 57, Issue 195, pp. 221 - 237
...) value problems for linear, ordinary, and partial differential equations. Restrictions on the stepsize are derived which guarantee the rate of error growth in these methods to be of moderate size... 
Approximation | Numerical analysis | Mathematical theorems | Partial differential equations | Heat equation | Eigenvalues | Polynomials | Recurrence relations | Cauchy problem | SEMIGROUPS | MATHEMATICS, APPLIED | STEPSIZE RESTRICTIONS | APPROXIMATIONS | BANACH-SPACES
Journal Article
NUMERISCHE MATHEMATIK, ISSN 0029-599X, 07/1992, Volume 62, Issue 2, pp. 235 - 267
It is well known that a necessary condition for the Lax-stability of the method of lines is that the eigenvalues of the spatial discretization operator, scaled... 
RESOLVENT CONDITION | MATRIX | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | STEPSIZE RESTRICTIONS | SPECTRAL METHODS
Journal Article
BIT, ISSN 0006-3835, 09/1991, Volume 31, Issue 3, pp. 482 - 528
In this paper we present necessary and sufficient conditions for Runge-Kutta methods to be contractive. We consider not only unconditional contractivity for... 
Subject Classifications: AMS (MOS): 65L05, 65L20, 65M10 | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | LINEAR MULTISTEP METHODS | STEPSIZE RESTRICTIONS | STABILITY | EQUATIONS | COMPUTER SCIENCE, SOFTWARE, GRAPHICS, PROGRAMMING | INITIAL-VALUE PROBLEMS | B-CONVERGENCE
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 1992, Volume 9, Issue 6, pp. 475 - 492
In this paper we present a necessary and sufficient condition for maximum norm contractivity of a large class of discretization methods for solving the heat... 
MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | STEPSIZE RESTRICTIONS | STABILITY | ABSOLUTE MONOTONICITY | INITIAL-VALUE PROBLEMS
Journal Article
Journal of computational physics, ISSN 0021-9991, 2007, Volume 225, Issue 2, pp. 1753 - 1781
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2010, Volume 53, Issue 2, pp. 261 - 280
.... When the stepsize is changed using the usual scaling procedure for Nordsieck methods, there can be adverse affects on the stability unless a severe restriction is placed on the allowable stepsize ratios... 
65L05 | 65L06 | Numeric Computing | Theory of Computation | L-stability | Variable stepsize | A-stability | Algebra | Algorithms | Computer Science | Mathematics, general | 65L20 | BDF methods | MATHEMATICS, APPLIED | STABILITY | Constrictions | Mathematical models | Numerical analysis | Stability
Journal Article
SIAM journal on numerical analysis, ISSN 0036-1429, 2015, Volume 53, Issue 2, pp. 701 - 719
Journal Article
SIAM journal on scientific computing, ISSN 1064-8275, 2003, Volume 24, Issue 3, pp. 848 - 864
...; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path. 
Embedding | SDEs | Runge-Kutta | Variable stepsize
Journal Article
SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2002, Volume 24, Issue 3, pp. 848 - 864
...; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path. 
MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | SDEs | SYSTEMS | Runge-Kutta | variable stepsize | embedding | ORDER CONDITIONS
Journal Article
Numerical Algorithms, ISSN 1017-1398, 12/2002, Volume 31, Issue 1, pp. 59 - 73
...)-stability behaviour. It is found that under this same restriction, A(α)-stability holds for α≈70°. For a new two stage two value first order method, which is L-stable for constant stepsize... 
A (α)-stability | Algebra | Algorithms | L -stability | Computer Science | Numeric Computing | Mathematics, general | A -stability | Theory of Computation | variable stepsize | multivalue methods | BDF methods | Multivalue methods | A(α)-stability | L-stability | Variable stepsize | A-stability | A(alpha)-stability | MATHEMATICS, APPLIED
Journal Article
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