A Laplace transform finite difference scheme for the Fisher-KPP equation
Journal of Algorithms & Computational Technology, 2021 This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform ...
Colin L Defreitas, Steve J Kane
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Staggered Finite Difference Schemes for Conservation Laws [PDF]
Journal of Scientific Computing, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gabriella Puppo, Giovanni Russo 0001
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Finite‐difference scheme for one problem of nonlinear optics
Mathematical Modelling and Analysis, 2008 We consider a mathematical model, which describes Q‐switching process. The finite difference scheme is developed for approximation of the given system of nonlinear PDEs.
Ingrida Laukaityte, Raimondas Čiegis
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Finite difference scheme for multi-term variable-order fractional diffusion equation
Advances in Difference Equations, 2018 In this paper, we consider a multi-term variable-order fractional diffusion equation on a finite domain, which involves the Caputo variable-order time fractional derivative of order α(x,t)∈(0,1) $\alpha(x,t) \in(0,1) $ and the Riesz variable-order space ...
Tao Xu +3 more
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Exact finite-difference scheme and nonstandard finite-difference scheme for coupled Burgers equation [PDF]
Advances in Difference Equations, 2014 Abstract This work develops exact finite-difference schemes for the two-dimensional nonlinear coupled viscous Burgers equation using the analytic solution. We extend the explicit nonstandard finite-difference schemes on the basis of the exact finite-difference schemes to solve the coupled Burgers equation.
Zhang, Lei, Wang, Lisha, Ding, Xiaohua
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A finite difference scheme for the two-dimensional sine-Gordon equation [PDF]
Delta Journal of ScienceThe sine-Gordon (SG) equation is a fundamental aspect of nonlinear physics. It models a wide range of phenomena in many scientific fields. While its mathematical structure allows analytical solutions under certain conditions, the complexity of real-world
A. Soliman +2 more
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Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 2023 In this work, we propose a new idea to improve numerical methods for solving partial differential equations (PDEs) through a deep learning approach.
Tatiana Kossaczká +2 more
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Numerical Solution of Parabolic Equations by the Box Scheme [PDF]
, 1973 The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic ...
Fong, Kirby William
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Efficient parallel computing with a compact finite difference scheme
, 2012 This paper proposes an efficient parallel computing approach based on a high-order accurate compact finite difference scheme in conjunction with a conventional domain decomposition method and MPI libraries.
Kim, J.W., Sandberg, R.D.
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Finite difference method on 1D and 2D Riemann problems for Euler equations with different state of equations [PDF]
, 2022 We discussed the finite difference WENO5 scheme on the 1D and 2D compressible Euler equations. The 1D Chaplygin gas system with a constant external force led to two kinds of solutions: contact discontinuity and delta shock.
Jin, Ling
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