scholarly journals Comparison of the exactness of several formulations of boundary conditions in the use of the finite difference method

1965 ◽  
Vol 10 (3) ◽  
pp. 302-307
Author(s):  
Karel Segeth
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
The Finite Difference Method

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%.

scholarly journals 1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods

2022 ◽  
Vol 7 ◽  
Author(s):  
Appanah R. Appadu ◽  
Yusuf O. Tijani
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Difference Method ◽  
Huxley Equation ◽  
The Finite Difference Method ◽  
A Minor

In this paper, we obtain the numerical solution of a 1-D generalised Burgers-Huxley equation under specified initial and boundary conditions, considered in three different regimes. The methods are Forward Time Central Space (FTCS) and a non-standard finite difference scheme (NSFD). We showed the schemes satisfy the generic requirements of the finite difference method in solving a particular problem. There are two proposed solutions for this problem and we show that one of the proposed solutions contains a minor error. We present results using FTCS, NSFD, and exact solution as well as show how the profiles differ when the two proposed solutions are used. In this problem, the boundary conditions are obtained from the proposed solutions. Error analysis and convergence tests are performed.

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