A Finite Difference Analog of the Neumann Problem for Poisson’s Equation

1965 ◽  
Vol 2 (1) ◽  
pp. 1-14 ◽  
Author(s):  
J. H. Bramble ◽  
B. E. Hubbard
Keyword(s):  
Finite Difference ◽  
Neumann Problem ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Difference Analog ◽  
The Neumann Problem ◽  
Finite Difference Analog

scholarly journals A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yaw Kyei ◽  
John Paul Roop ◽  
Guoqing Tang
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Three Dimensional ◽  
Difference Schemes ◽  
Poisson’S Equation ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Poisson's Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

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 stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.

A new finite difference representation for Poisson’s equation on from a contour integral

2010 ◽  
Vol 217 (8) ◽  
pp. 3624-3634 ◽  
Author(s):  
Anour F.A. Dafa-Alla ◽  
Kyung-Won Hwang ◽  
Soyoung Ahn ◽  
Philsu Kim
Keyword(s):  
Finite Difference ◽  
Poisson’S Equation ◽  
Contour Integral ◽  
Poisson's Equation
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