scholarly journals 1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods

Author(s):  
Appanah R. Appadu ◽  
Yusuf O. Tijani

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.

Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>


Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. W17-W26 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties.


2021 ◽  
Vol 133 (2) ◽  
pp. 31-33
Author(s):  
B. Z. Kazymov ◽  
◽  
Т. А. Samadov ◽  
S. H. Novruzova ◽  
E. V. Gadashova ◽  
...  

The problem of determining reservoir properties (porosity, permeability) of gas layers developed in the depletion mode, whose rocks are subjected to creeping deformation with the Abel core, is considered. In order to determine the parameters that characterize reservoir properties of the reservoir, the authors indicate the possibility of using an appropriate numerical solution to the problem of determining the theoretical values of the reservoir volume-weighted average reservoir pressures over time, obtained using the finite difference method.


1968 ◽  
Vol 90 (4) ◽  
pp. 773-776 ◽  
Author(s):  
R. Coleman

A noniterative finite difference method is given for the solutions of linear elliptic equations with linear boundary conditions. This method is applicable to a variety of gas bearing problems. Comparisons are made with other numerical techniques, and an application to the spiral groove thrust plate is given.


2018 ◽  
Vol 15 ◽  
pp. 8174-8184
Author(s):  
Sana'a Abdullah Alotibi

In this paper, a method to calculate tsunami wave front is introduced using the finite difference method to solve the ill-posed problem and to calculate perturbed velocity of the wave front. Comparison between the actual and approximate solution will be proposed in a table form and a graphic form.


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