A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

2018 ◽  
Vol 11 (08) ◽  
pp. 1850099 ◽  
Author(s):  
Mohamed M. Khader ◽  
Khaled M. Saad
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Collocation Method ◽  
Numerical Study ◽  
Fisher Equation ◽  
Chebyshev Collocation Method ◽  
The Third ◽  
The Finite Difference Method

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

scholarly journals Modified Chebyshev Collocation Method for Solving Differential Equations

CAUCHY ◽  
2015 ◽  
Vol 3 (4) ◽  
pp. 208
Author(s):  
M Ziaul Arif ◽  
Ahmad Kamsyakawuni ◽  
Ikhsanul Halikin
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Collocation Method ◽  
Difference Method ◽  
Numerical Scheme ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Polynomial Collocation

This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial) collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial) collocation method is applied to both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon

2017 ◽  
Vol 743 ◽  
pp. 449-453
Author(s):  
Vladimir Arkhipov ◽  
Alexander Nee ◽  
Lily Valieva
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Phase Transitions ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mathematical Modelling ◽  
Three Dimensional ◽  
Two Phase ◽  
One Dimensional ◽  
The Finite Difference Method

This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

Numerical Simulation for DC PD in Void

2013 ◽  
Vol 448-453 ◽  
pp. 1982-1987
Author(s):  
Jin Zhong Li ◽  
Shu Qi Zhang ◽  
Rui Guo ◽  
Hao Tang ◽  
Tao Zhao ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Repetition Rate ◽  
Electric Field Distribution ◽  
Time Interval ◽  
Stochastic Property ◽  
Dc Voltage ◽  
The Finite Difference Method ◽  
The Relationship

A numerical simulation for DC PD in void is put forward based on the PD physical process. The finite difference method is used to calculate the electric field distribution, and both of the stochastic property and the accumulation of the charge after PD on the void surfaces are considering in the model. The time of PD occurring, the amount of discharge and the voltage across the void are calculated. Meanwhile, the relationship between the DC voltage and the PD time interval or repetition rate is also simulation, the results show that with the increase of the DC voltage, the PD interval corresponding decreases exponentially and the repetition rate increases exponentially.

Clamped-Free Single-Walled Carbon Nanotube-Based Mass Sensor Treated as Bernoulli–Euler Beam

2011 ◽  
Vol 2 (2) ◽  
Author(s):  
I. Elishakoff ◽  
C. Versaci ◽  
N. Maugeri ◽  
G. Muscolino
Keyword(s):  
Exact Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mass Sensor ◽  
Euler Beam ◽  
Attached Bacterium ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
The Finite Difference Method

In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference method, and the Bubnov–Galerkin method.

Numerical Simulation of Consolidation Test Considering Different Drainage Height

2012 ◽  
Vol 170-173 ◽  
pp. 2325-2328
Author(s):  
Yang Liu ◽  
Zhe Wang
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Soil Sample ◽  
Difference Method ◽  
Simulation Method ◽  
Test Apparatus ◽  
Consolidation Test ◽  
Simulation Results ◽  
The Finite Difference Method

Numerical simulation of the consolidation test was developed in different drainage conditions using the finite difference method. Soil sample was divided into layers to determine the time-steps of the test. A series of simulation tests were carried out to study the influence of drainage height on the coefficient ratio. Finally, some experiments data were compared with the numerical simulation results. Numerical results indicate that the simulation method broke through the limitation of test apparatus, and made it possible to conduct big size specimen consolidation test under certain conditions.

scholarly journals Buckling of double-walled carbon nanotubes

2012 ◽  
Vol 34 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Isaac Elishakoff ◽  
Kévin Dujat ◽  
Maurice Lemaire
Keyword(s):  
Carbon Nanotubes ◽  
Exact Solution ◽  
Approximate Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Simply Supported ◽  
The Finite Difference Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this note we deal with the approximate solution of the buckling problem of a clamped-free double-walled carbon nanotube. First the finite difference method is utilized to solve this case. Then this approach is verified by solving the buckling problem of a double-walled carbon nanotube that is simply supported at both ends for which the exact solution is available.

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