Results 1 to 10 of about 1,147,753 (236)
Journal of Applied Mathematics, 2014 We present finite difference schemes for Burgers equation and Burgers-Fisher equation. A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution.
Lei Zhang, Lisha Wang, Xiaohua Ding
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A compact finite difference scheme with absorbing boundary condition for forced KdV equation [PDF]
MethodsX, 2023 Studying the long-time solution behavior of the Korteweg-de Vries (KdV) type equation with a periodic force acting at one end of the long channel is important for simulating the blood flow in artery driven by heart pulses.
Jiaqi Chen, Weizhong Dai
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A conservative finite difference scheme for Poisson–Nernst–Planck equations [PDF]
Journal of Computational Electronics, 2013 A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson–Nernst–Planck (PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, second-order accurate in both space and time.
Allen Flavell +5 more
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A dynamically-consistent nonstandard finite difference scheme for the SICA model [PDF]
Mathematical biosciences and engineering : MBE, 2021 In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible-Infected-Chronic-AIDS) model and analyze the dynamical properties of the discretized system.
Sandra Vaz, Delfim F. M. Torres
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Numerical solutions for a class stochastic partial differential equations [PDF]
Journal of Mahani Mathematical Research, 2023 The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme.
Mehdi Karami +4 more
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Recursive finite-difference Lattice Boltzmann schemes [PDF]
Computers & Mathematics with Applications, 2021 The motivation of this study is twofold. First, a recursive mathematical formulation of the discrete-velocity Boltzmann equation (DVBE) under the Bhatnagar-Gross-Krook (BGK) approximation is introduced. This formulation allows us to formally express the solution of the DVBE as an infinite sum over successive particle derivatives of the distributions ...
Vienne, Lucien, Lévêque, Emmanuel
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Finite Difference formulation of any lattice Boltzmann scheme [PDF]
Numerische Mathematik, 2022 Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase.
T. Bellotti, B. Graille, M. Massot
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Advances in Differential Equations, 2021 The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the
D. Baleanu +3 more
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Fractal and Fractional, 2023 The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
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A Generalized Finite Difference Scheme for Multiphase Flow
Mathematical and Computational Applications, 2023 This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated.
Johannes C. Joubert +2 more
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