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.

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 Solution of the Porous Media Equation by a Compact Finite Difference Method

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Murat Sari
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Exact Solutions ◽  
Difference Method ◽  
Numerical Solutions ◽  
Porous Media Equation ◽  
Compact Finite Difference ◽  
Media Equation ◽  
Compact Finite Difference Method

Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. Therefore, this scheme causes to less accumulation of numerical errors and less use of storage space. The computed results obtained by this way have been compared with the exact solutions to show the accuracy of the method. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. This method is seen to be a very good alternative method to some existing techniques for such realistic problems.

scholarly journals Construction of a Class of Copula Using the Finite Difference Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Remi Guillaume Bagré ◽  
Frédéric Béré ◽  
Vini Yves Bernadin Loyara
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Scheme ◽  
Approximate Solutions ◽  
Copula Function ◽  
Common Technique ◽  
The Finite Difference Method ◽  
Definition Of ◽  
General Method

The definition of a copula function and the study of its properties are at the same time not obvious tasks, as there is no general method for constructing them. In this paper, we present a method that allows us to obtain a class of copula as a solution to a boundary value problem. For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.

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

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