A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation
نویسندگان
چکیده
منابع مشابه
A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation
We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson’s equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson’s equation on a compact st...
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This work extends the previous two-dimensional compact scheme for the Cahn–Hilliard equation (Lee et al., 2014) to three-dimensional space. The proposed scheme, derived by combining a compact formula and a linearly stabilized splitting scheme, has second-order accuracy in time and fourth-order accuracy in space. The discrete system is conservative and practically stable. We also implement the c...
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In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...
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Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...
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ژورنال
عنوان ژورنال: Advances in Numerical Analysis
سال: 2010
ISSN: 1687-9562,1687-9570
DOI: 10.1155/2010/352174