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Compact Finite Difference Schemes for Approximating Differential Relations
Mathematical Models and Computer Simulations, 2020Differential relations include both differential operators and solvers for boundary value problems. The formulas of compact finite difference approximations for first- and second-order differential relations of the form $${{P}_{1}}[u] = {{P}_{2}}[f]$$ are obtained. An approximation on three-point stencils is used.
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Some Stability Inequalities for Compact Finite Difference Schemes
Mathematische Nachrichten, 1988AbstractFor finite difference schemes of compact form on nonuniform grids approximating m‐th order two‐point boundary value problems stability inequalities are proved which use a norm analogous to the Spijker‐norm in the case of multistep methods. The results are applied to a number of finite difference schemes for which they establish a higher order ...
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Generalized finite compact difference scheme for schock/complex flowfield interaction.
40th Fluid Dynamics Conference and Exhibit, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shen, Yiqing, Zha, Gecheng
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Compact fourth-order finite difference method for solving differential equations
Physical Review E, 2001We present a fourth-order finite difference (FD) method for solving two-dimensional partial differential equations. The FD operator uses a compact nine-point stencil on a regular square grid. Despite the regular grid, Dirichlet boundary conditions can be applied on an arbitrarily shaped boundary without resorting to the usual stepped approximation.
P B, Wilkinson +4 more
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Optimised boundary compact finite difference schemes for computational aeroacoustics
Journal of Computational Physics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A predictor–corrector compact finite difference scheme for Burgers’ equation
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Pei-Guang, Wang, Jian-Ping
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Numerical Methods for Partial Differential Equations, 2019
In this paper, a compact finite difference scheme is constructed and investigated for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel.
Da Xu, W. Qiu, Jing Guo
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In this paper, a compact finite difference scheme is constructed and investigated for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel.
Da Xu, W. Qiu, Jing Guo
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Compact Finite Difference Schemes for Mixed Initial-Boundary Value Problems
SIAM Journal on Numerical Analysis, 1982This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of energy arguments and both types of equations are solved by similar algorithms.
Philips, Richard B., Rose, Milton E.
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, 2020
Three semi-implicit compact finite difference schemes are described for the nonlinear partial integro-differential equation arising from viscoelasticity.
Xuan Zheng, W. Qiu, Hongbin Chen
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Three semi-implicit compact finite difference schemes are described for the nonlinear partial integro-differential equation arising from viscoelasticity.
Xuan Zheng, W. Qiu, Hongbin Chen
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Numerical Methods for Partial Differential Equations, 2020
Two fourth‐order compact finite difference schemes including a Crank–Nicolson one and a semi‐implicit one are derived for solving the nonlinear Klein–Gordon equations in the nonrelativistic regime. The optimal error estimates and the strategy in choosing
Tengren Zhang, Ting-chun Wang
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Two fourth‐order compact finite difference schemes including a Crank–Nicolson one and a semi‐implicit one are derived for solving the nonlinear Klein–Gordon equations in the nonrelativistic regime. The optimal error estimates and the strategy in choosing
Tengren Zhang, Ting-chun Wang
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