Convergence of the Finite-Difference Method for the 1—d Wave Equation with Homogeneous Dirichlet Boundary Conditions

2013 ◽  
pp. 59-78
Author(s):  
Sylvain Ervedoza ◽  
Enrique Zuazua
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
The Finite Difference Method ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
D Wave

Some refinements on the finite‐difference method for 3-D dc resistivity modeling

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1301-1307 ◽  
Author(s):  
Shengkai Zhao ◽  
Matthew J. Yedlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Dirichlet Boundary Conditions ◽  
Percentage Error ◽  
Dc Resistivity ◽  
The Finite Difference Method ◽  
Vertical Contact ◽  
Resistivity Modeling

Two basic refinements of the finite‐difference method for 3-D dc resistivity modeling are presented. The first is a more accurate formula for the source singularity removal. The second is the analytic computation of the source terms that arise from the decomposition of the potential into the primary potential because of the source current and the secondary potential caused by changes in the electrical conductivity. Three examples are presented: a simple two‐layered model, a vertical contact, and a buried sphere. Both accurate and approximate Dirichlet boundary conditions are used to compute the secondary potential. Numerical results show that for all three models, the average percentage error of the apparent resistivity obtained by the modified finite‐difference method with accurate boundary conditions is less than 0.5%. For the vertical contact and the buried sphere models, the error caused by the approximate boundary condition is less than 0.01%.

Finite Difference Method with Dirichlet Problems of 2D Laplace’s Equation in Elliptic Domain

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Ubaid Ullah ◽  
Muhammad Saleem Chandio
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Dirichlet Boundary ◽  
Numerical Solutions ◽  
Rectangular Domain ◽  
Dirichlet Boundary Conditions ◽  
Dirichlet Problems ◽  
Study Objective

<p>In this study finite difference method (FDM) is used with Dirichlet boundary conditions on rectangular domain to solve the 2D Laplace equation. The chosen body is elliptical, which is discretized into square grids. The finite difference method is applied for numerical differentiation of the observed example of rectangular domain with Dirichlet boundary conditions. The obtained numerical results are<br />compared with analytical solution. The obtained results show the efficiency of the FDM and settled with the obtained exact solution. The study objective is to check the accuracy of FDM for the numerical solutions of elliptical bodies of 2D Laplace equations. The study contributes to find the heat (temperature) distribution inside a regular rectangular elliptical discretized body.</p>

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