Corrigendum to: “A Matlab-based finite difference solver for the Poisson problem with mixed Dirichlet–Neumann boundary conditions” [Comput. Phys. Comm. 184(3) (2013) 783–798]

2016 ◽  
Vol 209 ◽  
pp. 200-201
Author(s):  
Ashton S. Reimer ◽  
Alexei F. Cheviakov
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Poisson Problem ◽  
Comput Phys

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

scholarly journals Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Asma Yosaf ◽  
Shafiq Ur Rehman ◽  
Fayyaz Ahmad ◽  
Malik Zaka Ullah ◽  
Ali Saleh Alshomrani
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Eighth Order ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method

The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D) heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.

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