Results 51 to 60 of about 12,386 (163)
Solution of convection–diffusion equation by the method of characteristics
Journal of Computational and Applied Mathematics, 2004 The author considers the nonlinear problem: \[ \partial_tu+ F(u) \nabla u-D\Delta u=0;\quad u(0,x)= u_0(x)\;x\in\Omega \] with homogeneous boundary conditions. This problem is solved by the method of characteristics. One of the innovations in the paper is that the velocity field must not be bounded, it is enough to be supposed continuous.
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An Efficient Numerical Model for the Black–Scholes Equations
Journal of Applied MathematicsIn this paper, a novel numerical model for the Black–Scholes equations is developed. To address some potential issues that may arise when solving this equation using the conventional model, the original Black–Scholes equation is reformulated as a ...
Yan Zhou, Yunxing Zhang
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A monotone finite-difference high order accuracy scheme for the 2D convection – diffusion equations
Журнал Белорусского государственного университета: Математика, информатика, 2019 A stable finite-difference scheme is constructed on a minimum stencil of a uniform mesh for a two-dimensional steady-state convection – diffusion equation of a general form; the scheme is theoretically studied and tested.
Viktor K. Polevikov
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Modelling of the Czochralski flow
Abstract and Applied Analysis, 1998 The Czochralski method of the industrial production of a silicon single crystal consists of pulling up the single crystal from the silicon melt. The flow of the melt during the production is called the Czochralski flow.
Jan Franc
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Advances in Difference Equations, 2019 This paper addresses exponential basis and compact formulation for solving three-dimensional convection-diffusion-reaction equations that exhibit an accuracy of order three or four depending on exponential expanding or uniformly spaced grid network.
Navnit Jha, Bhagat Singh
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EXACT SOLUTIONS OF THE ONE-DIMENSIONAL CONVECTION-DIFFUSION EQUATION USING LIE GROUP METHOD [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2017 Lie symmetry group analysis is applied to determine the exact solution of the one-dimensional convection-diffusion equation. The similarity transformation is found using symmetries, and the invariant solution of the original partial differential ...
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Advances in Nonlinear AnalysisThis work is devoted to study the convection–reaction–diffusion behavior of contaminant in the recovered fracturing fluid which flows in the wellbore from shale gas reservoir. First, we apply various constitutive laws for generalized non-Newtonian fluids,
Cen Jinxia +3 more
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Electrochemistry CommunicationsNatural convection could arise even at ultra-low redox concentration solutions (1–10 mM). Models such as convection–diffusion layer model and spontaneous convection model have been established to describe this phenomenon.
Zichen Zhang +6 more
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On the Generalized Fractional Convection–Diffusion Equation with an Initial Condition in
Fractal and FractionalTime-fractional convection–diffusion equations are significant for their ability to model complex transport phenomena that deviate from classical behavior, with numerous applications in anomalous diffusion, memory effects, and nonlocality.
Chenkuan Li +3 more
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Convection–diffusion equations in a circle: The compatible case
Journal de Mathématiques Pures et Appliquées, 2011 The authors consider the following 2D singular perturbation problem \[ \begin{cases}-\varepsilon \Delta u^{\varepsilon}-\partial_y u^{\varepsilon}=f(x,y) &\text{in } D,\\ u^{\varepsilon}=0 &\text{on } \partial D,\end{cases}\tag{E} \] where \(D\) is the unit disc \(D=\{(x,y): x^2+y^2\leq 1\}\). They study the convergence of the family \(u^{\varepsilon}\)
Jung, Chang-Yeol, Temam, Roger
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