scholarly journals Generalization of the Exact Solution of 1D Poisson Equation with Robin Boundary Conditions, Using the Finite Difference Method

2014 ◽  
Vol 06 (12) ◽  
pp. 372-381
Author(s):  
Serigne Bira Gueye ◽  
Kharouna Talla ◽  
Cheikh Mbow
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Poisson Equation ◽  
Difference Method ◽  
Robin Boundary Conditions ◽  
The Finite Difference Method ◽  
Robin Boundary

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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