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Wavelet-optimized compact finite difference method for convection–diffusion equations
International Journal of Nonlinear Sciences and Numerical Simulation, 2020Abstract In this article, compact finite difference approximations for first and second derivatives on the non-uniform grid are discussed. The construction of diffusion wavelets using compact finite difference approximation is presented.
Mani Mehra +2 more
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Communication on Applied Mathematics and Computation, 2023
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations, we show that the simple bound-preserving limiter in Li et al ...
Hao Li, Xiangxiong Zhang
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For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations, we show that the simple bound-preserving limiter in Li et al ...
Hao Li, Xiangxiong Zhang
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International Journal of Computational Mathematics, 2022
In this paper, the correction for the remainder of the truncation error of the second-order central difference scheme is employed to discretize temporal derivative, while the fourth-order Padé schemes are directly used to compute spatial derivatives, an ...
Yunzhi Jiang, Y. Ge
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In this paper, the correction for the remainder of the truncation error of the second-order central difference scheme is employed to discretize temporal derivative, while the fourth-order Padé schemes are directly used to compute spatial derivatives, an ...
Yunzhi Jiang, Y. Ge
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Mathematical methods in the applied sciences, 2021
In this paper, the multi‐term time fractional mixed diffusion and diffusion‐wave equation is investigated. Firstly, a compact finite difference scheme with fourth‐order spatial accuracy and high‐order temporal accuracy is derived. Then, the unconditional
Bo Yu
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In this paper, the multi‐term time fractional mixed diffusion and diffusion‐wave equation is investigated. Firstly, a compact finite difference scheme with fourth‐order spatial accuracy and high‐order temporal accuracy is derived. Then, the unconditional
Bo Yu
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Two‐dimensional compact finite difference immersed boundary method
International Journal for Numerical Methods in Fluids, 2011AbstractWe present a compact finite differences method for the calculation of two‐dimensional viscous flows in biological fluid dynamics applications. This is achieved by using body‐forces that allow for the imposition of boundary conditions in an immersed moving boundary that does not coincide with the computational grid.
Ferreira de Sousa, Paulo J. S. A. +2 more
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Compact analytic expressions of two‐dimensional finite difference forms
International Journal for Numerical Methods in Engineering, 1984AbstractIn this paper a straightforward derivation of one‐ and two‐dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem ...
Reali, M., Rangogni, R., Pennati, V.
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Compact finite difference method for integro-differential equations
Applied Mathematics and Computation, 2006The paper is concerned with developing a method for the approximate solution of (Fredholm) integro-differential equations. The authors remark that the method proposed can also be applied to Volterra equations. The starting point is a compact finite difference scheme for the second order derivatives.
Zhao, Jichao, Corless, Robert M.
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Optimized compact finite difference schemes with maximum resolution
AIAA Journal, 1996Direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high-resolution characteristics in the evaluation of spatial derivatives. Compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation ...
Kim, J.W., Lee, D.J.
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Upwind compact finite difference schemes
Journal of Computational Physics, 1985It was shown by \textit{M. Ciment}, \textit{S. H. Leventhal}, and \textit{B. C. Weinberg} [J. Comput. Phys. 28, 135-166 (1978; Zbl 0393.65038)] that the standard compact finite difference scheme may break down in convection dominated problems. An upwinding of the method, which maintains the fourth order accuracy, is suggested and favorable numerical ...
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A fast compact finite difference scheme for the fourth-order diffusion-wave equation
International Journal of Computational MathematicsIn this paper, the H $ {}_2 $ 2N $ {}_2 $ 2 method and compact finite difference scheme are proposed for the fourth-order time-fractional diffusion-wave equations.
Wan Wang +3 more
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