Numerical solution of the nonlinear Poisson equation for semiconductor devices by application of a diffusion-equation finite difference scheme

2008 ◽  
Vol 104 (6) ◽  
pp. 063715 ◽  
Author(s):  
Alina Jóźwikowska
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Poisson Equation ◽  
Finite Difference Scheme ◽  
Semiconductor Devices

scholarly journals Computationally Efficient Hybrid Method for the Numerical Solution of the 2D Time Fractional Advection-Diffusion Equation

2020 ◽  
Vol 5 (3) ◽  
pp. 432-446
Author(s):  
Fouad Mohammad Salama ◽  
Norhashidah Hj. Mohd Ali
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Hybrid Method ◽  
Finite Difference Scheme ◽  
Computational Cost ◽  
Stability And Convergence ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

In this paper, a hybrid method based on the Laplace transform and implicit finite difference scheme is applied to obtain the numerical solution of the two-dimensional time fractional advection-diffusion equation (2D-TFADE). Some of the major limitations in computing the numerical solution for fractional differential equations (FDEs) in multi-dimensional space are the huge computational cost and storage requirement, which are O(N^2) cost and O(MN) storage, N and M are the total number of time levels and space grid points, respectively. The proposed method reduced the computational complexity efficiently as it requires only O(N) computational cost and O(M) storage with reasonable accuracy when numerically solving the TFADE. The method’s stability and convergence are also investigated. The Results of numerical experiments of the proposed method are obtained and found to compare well with the results of existing standard finite difference scheme.

Finite difference scheme for solving general 3D convection–diffusion equation

2004 ◽  
Vol 164 (1-3) ◽  
pp. 318-329 ◽  
Author(s):  
N. McTaggart ◽  
R. Zagórski ◽  
X. Bonnin ◽  
A. Runov ◽  
R. Schneider
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Convection Diffusion ◽  
Convection Diffusion Equation
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