On the Construction and Comparison of Difference Schemes

By G. Strang. 1968

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Citations in the corpus

Understanding and mitigating gradient pathologies in physics-informed neural networks (2020, background): “From a numerical analysis standpoint, it is then natural to investigate whether more stable discretizations, such as implicit or IMEX operator splitting schemes [30, 35], can yield more effective optimization algorithms for constrained neural networks.”
Numerical methods for kinetic equations* (2014, background): “G. Strang (1968), ‘On the construction and the comparison of difference schemes’, SIAM J. Numer.”
The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines (2009, methodology): “We follow IT in using a second-order accurate splitting method by performing a Strang symmetrisation (see Strang (1968)) for the splitting method which uses the CrankNicolson method.”
Score-Based Generative Modeling with Critically-Damped Langevin Diffusion (2021, unknown): “Using the symmetric Trotter theorem or Strang splitting formula as well as the Baker–Campbell–Hausdorff formula (Trotter, 1959; Strang, 1968; Tuckerman, 2010), it can be shown that: et(L̂ ∗ A+L̂S) = lim N→∞ [ e δt 2 L̂∗AeδtL̂ ∗ Se δt 2 L̂A ]N ≈ [ e δt 2 L̂∗AeδtL̂ ∗ Se δt 2 L̂A ]N +O(Nδt(3)), (11) fo”
Three-dimensional simulations of core-collapse supernovae: from shock revival to shock breakout (2014, methodology): “It solves the multidimensional Newtonian hydrodynamic equations using dimensional splitting (Strang 1968), piecewise parabolic reconstruc- tion (PPM; Colella & Woodward 1984), a Riemann solver for real gases (Colella & Glaz 1985), and the consistent multifluid advection scheme (CMA; Plewa & Müller…”
A split step approach for the 3-D Maxwell's equations (2003, methodology): “One obtains second-order accuracy in time by instead alternating the two equations in the pattern A, B, A while using the time increments { 1 4 , 1 2 , 1 4 } - known as “Strang splitting” [12].”
High-order multi-implicit spectral deferred correction methods for problems of reactive flow (2003, methodology): “accurate than OðDt(2)Þ locally and OðDtÞ globally, regardless of the order of the integration errors [23].”
COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY (2007, methodology): “2 Strang symmetrized splitting method A second-order accurate splitting method can be achieved by performing a Strang symmetrization [31] for the splitting method (32) which uses the Crank-Nicolson method.”
Planetary waves in coupling the lower and upper atmosphere (2007, methodology): “To integrate the prognostic equations, the initial Cauchy problem was split (Marchuk, 1967; Strang, 1968) into a set of simpler problems according to the physical processes considered, which in our case are vertical diffusion of momentum and heat on the one hand, and all remaining processes on the o”
Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems (2005, methodology): “The most common second-order operatorsplitting methods of this type are those of Strang [14] and Marchuk [9].”
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations (2003, methodology): “Either alternation or symmetrization, as first proposed by Strang [48], is usually used to preserve the accuracy of the second-order 1D method and reduce grid alignment effects.”
Finite Element Methods for the Incompressible Navier-Stokes Equations (2000, methodology): “The symmetric form of this scheme follows the ideas from Strang [87], in order to achieve a second-order splitting approximation.”
Volume filling factors of the ISM phases in star forming galaxies. I. The role of the disk-halo interaction (2004, methodology): “…of the code uses the piecewiseparabolic method of Colella & Woodward (1984), a thirdorder scheme based on a Godunov method implemented in a dimensionally-split manner (Strang 1968) that relies on solutions of the Riemann problem in each zone rather than on artificial viscosity to follow shocks.”