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Strong stability preserving second derivative multistep methods
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pari Khakzad +3 more
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A Polynomial Formulation of Adaptive Strong Stability Preserving Multistep Methods
SIAM Journal on Numerical Analysis, 2019The task of this paper is to develop a methodology that allows to formulate a given strong stability preserving multistep method as a variable step-size method. In particular, this is here done for time-dependent partial differential equations. The method is flexible to various step-size selection criteria and may be combined with traditional error ...
Fatemeh Mohammadi +2 more
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Characterizing Strong Stability Preserving Additive Runge-Kutta Methods
Journal of Scientific Computing, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Strong Stability Preserving Explicit Peer Methods for Discontinuous Galerkin Discretizations
Journal of Scientific Computing, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcel Klinge, Rüdiger Weiner
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Representations of Runge--Kutta Methods and Strong Stability Preserving Methods
SIAM Journal on Numerical Analysis, 2005The Shu-Osher representation is a useful tool for the investigation of monotone high-order explicit Runge-Kutta methods. In the paper under review, this idea is extended to arbitrary Runge-Kutta methods. Particular attention is paid to the question of finding the optimal step size restriction.
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Rosenbrock strong stability-preserving methods for convection–diffusion–reaction equations
Japan Journal of Industrial and Applied Mathematics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hai, Doan Duy, Yagi, Atsushi
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Strong Stability Preserving Time Discretizations: A Review
2015Strong stability preserving (SSP) high order time discretizations were developed to address the need for nonlinear stability properties in the numerical solution of hyperbolic partial differential equations with discontinuous solutions. These methods preserve the monotonicity properties (in any norm, seminorm or convex functional) of the spatial ...
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Strong stability preserving Runge-Kutta projection methods
When solving nonlinear hyperbolic partial differential equations, such as compressible Euler equations, discontinuities may arise even with smooth initial conditions. To ensure convergence to the physically meaningful solution in the presence of discontinuities it is necessary to impose a nonlinear stability condition on the numerical solution.Najafian, Mohammad R. +1 more
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Fitted strong stability-preserving schemes for the Black-Scholes-Barenblatt equation
International Journal of Computer Mathematics, 2015We solve numerically a fully nonlinear Black–Scholes problem of Bellman type. The algorithm is focused on the so-called Delta greek, the first spatial derivative of the option price. Since the elliptic operator degenerates on the boundary we use a fitted finite volume discretization in space. Strong stability-preserving time-marching is further applied
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Strong stability preserving general linear methods
AIP Conference Proceedings, 2023Giovanna Califano +2 more
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