Qualitatively Stable Schemes for the Black–Scholes Equation
Fractal and Fractional, 2023 In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and
Mohammad Mehdizadeh Khalsaraei +5 more
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Experiments with a Positivity-Preserving Operator [PDF]
Experimental Mathematics, 2008 We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse of this operator to the rational functions.
Manuel Kauers, Doron Zeilberger
openaire +3 more sources
Positivity preserving results for a biharmonic equation under Dirichlet boundary conditions [PDF]
Opuscula Mathematica, 2014 We prove a dichotomy result giving the positivity preserving property for a biharmonic equation with Dirichlet boundary conditions arising in MEMS models. We adapt some ideas in [H.-Ch. Grunau, G.
Hanen Ben Omrane, Saïma Khenissy
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Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part II: The multidimensional case [PDF]
Journal of Computational Physics, 2022 In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the chemically reacting ...
Eric J. Ching +2 more
semanticscholar +1 more source
A high order positivity-preserving polynomial projection remapping method
Journal of Computational Physics, 2023 In this paper, we develop a high-order positivity-preserving polynomial projection remapping method based on the L projection for the discontinuous Galerkin (DG) scheme.
Nuo Lei, Juan Cheng, Chi-Wang Shu
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A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows [PDF]
Journal of Computational Physics, 2021 We present a robust, highly accurate, and efficient positivityand boundedness-preserving diffuse interface method for the simulations of compressible gas-liquid two-phase flows with the five-equation model by Allaire et al.
M. Wong +3 more
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Some standard and nonstandard finite difference schemes for a reaction–diffusion–chemotaxis model
Open Physics, 2023 Two standard and two nonstandard finite difference schemes are constructed to solve a basic reaction–diffusion–chemotaxis model, for which no exact solution is known.
de Waal Gysbert Nicolaas +2 more
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A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations [PDF]
14th WCCM-ECCOMAS Congress, 2021 In this paper, we present a positivity-preserving limiter for nodal Discontinuous Galerkin disctretizations of the compressible Euler equations. We use a Legendre-Gauss-Lobatto (LGL) Discontinuous Galerkin Spectral Element Method (DGSEM) and blend it ...
A. M. Rueda-Ramírez, G. Gassner
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An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion
Mathematics, 2022 In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary ...
Mikhail K. Kolev +2 more
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Journal of Computational Physics, 2023 This paper studies three high-order structure-preserving finite volume weighted essentially non-oscillatory (WENO) methods, which are not only well balanced (WB) for a general known hydrostatic equilibrium state but also preserve the positivity of density
Yupeng Ren, Kailiang Wu, J. Qiu, Y. Xing
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