scholarly journals Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method

2015 ◽  
Vol 11 (2) ◽  
pp. 57-67 ◽  
Author(s):  
B. İnan ◽  
A. R. Bahadir
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Linear Equations ◽  
System Of Nonlinear Equations ◽  
Time Step ◽  
Gauss Elimination ◽  
Huxley Equation ◽  
A New Technique

Abstract In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then linear equations system is obtained. Finally, linear equations system is solved using Gauss elimination method at each time-step. The numerical solutions obtained by this way are compared with the exact solutions and obtained by other methods to show the efficiency of the method.

scholarly journals A New Numerical Scheme for the Generalized Huxley Equation

2016 ◽  
Vol 16 ◽  
pp. 105-111
Author(s):  
Bilge Inan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Exact Solutions ◽  
Difference Method ◽  
Present Method ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Alternative Method ◽  
Huxley Equation

In this paper, an implicit exponential finite difference method is applied to compute the numerical solutions of the nonlinear generalized Huxley equation. The numerical solutions obtained by the present method are compared with the exact solutions and obtained by other methods to show the efficiency of the method. The comparisons showed that proposed scheme is reliable, precise and convenient alternative method for solution of the generalized Huxley equation.

Numerical solutions to a fractional diffusion equation used in modelling dye-sensitized solar cells

2021 ◽  
Vol 63 ◽  
pp. 420-433
Author(s):  
Benjamin J. Maldon ◽  
Bishnu Lamichhane ◽  
Ngamta Thamwattana
Keyword(s):  
Solar Cells ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Dye Sensitized Solar Cells ◽  
Fractional Diffusion ◽  
Operating Efficiency ◽  
Dye Sensitized ◽  
Sensitized Solar Cells

Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement. doi:10.1017/S1446181121000353

scholarly journals On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Robin Elliptic Boundary Value Problem

2019 ◽  
Vol 11 (1) ◽  
pp. 26
Author(s):  
Germain Nguimbi ◽  
Diogène Vianney Pongui Ngoma ◽  
Vital Delmas Mabonzo ◽  
Bienaime Bervi Bamvi Madzou ◽  
Melchior Josièrne Jupy Kokolo
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Simulations ◽  
Difference Method ◽  
Numerical Solutions ◽  
Classical Method ◽  
Elliptic Boundary ◽  
Boundary Condi Tions ◽  
Elliptic Boundary Value ◽  
Uniqueness Of The Solution

This paper refers to mathematical modelling and numerical analysis. The analysis to be presented through this paper deals with Robin’s problem which boundary equation is a linear combination of Dirichlet and Neumann-type boundary condi-tions. For this purpose we proved the existence and uniqueness of the solution. It is worth noting that the implementation of numerical simulations depends on the type of problem since it requires a search for explicit solution. Consequently, the motivation exists in this paper for choosing a classical method of variation of constants and employing a finite difference method to find the exact and numerical solutions, respectively so that numerical simulations were implemented in Scilab.

scholarly journals Numerical Investigation of the Unsteady Flows in Hydropower Plants

2021 ◽  
pp. 1-7
Author(s):  
Roozbeh Aghamagidi ◽  
Mohammad Emami ◽  
Dariush Firooznia
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Coefficient Of Friction ◽  
Difference Method ◽  
Characteristic Method ◽  
Fast Wave ◽  
Time Step ◽  
Characteristic Lines ◽  
Implicit Finite Difference ◽  
Implicit Finite Difference Method

One of the most important hazards that threatens the stability of power plant buildings is the phenomenon of water hammer, which can occur in the Penstock pipe of a turbine due to the rapid opening and closing of a valve. Fluid Descriptive Equations in this situation, there are two hyperbolic partial nonlinear partial differential equations that are very difficult and complex to solve analytically and are possible only for very simple conditions. In this study, by examining the two numerical methods of characteristic lines and implicit finite difference with Verwy & Yu schema, which are widely used in the analysis of instabilities, their disadvantages and advantages are clearly clarified and a suitable comparison basis for use. They should be provided in different conditions in hydropower plant. The results of the characteristic method in terms of maximum and minimum pressure show more and less values than the implicit finite difference method. In the characteristic method, perturbations and fast wave fronts are presented with more accuracy than the implicit finite difference method. At points near the upstream, downstream and middle boundaries, the accuracy of the characteristic method in presenting pressure and flow fluctuations is higher than the implicit finite difference method. In the characteristic method, it is recommended not to use certain time steps and try as much as possible avoid interpolation by selecting the appropriate time step. The results of examining the amount of changes in coefficient of friction in both methods show that it is not correct to take its value constant (proportional to the value obtained in stable conditions) and coefficient of friction should be calculated in proportion to changes in velocity at different times and used in the governing equation.

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