scholarly journals On a semi-implicit numerical method for the surface diffusion equation for triangulated surfaces

2021 ◽  
Vol 18 (2) ◽  
pp. 1367-1389
Author(s):  
Yu. D. Efremenko
Keyword(s):  
Diffusion Equation ◽  
Numerical Method ◽  
Surface Diffusion ◽  
Triangulated Surfaces ◽  
Implicit Numerical Method

scholarly journals ANALISIS KONVERGENSI METODE BEDA HINGGA DALAM MENGHAMPIRI PERSAMAAN DIFUSI

2018 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
F. MUHAMMAD ZAIN ◽  
M. GARDA KHADAFI ◽  
P. H. GUNAWAN
Keyword(s):  
Diffusion Equation ◽  
Numerical Method ◽  
Taylor Expansion ◽  
Separation Of Variables ◽  
Second Derivative ◽  
Linear Type ◽  
Spatial Error ◽  
Numerical Convergence ◽  
Result Show ◽  
Good Agreement

The diffusion equation or known as heat equation is a parabolic and linear type of partial differential equation. One of the numerical method to approximate the solution of diffusion equations is Finite Difference Method (FDM). In this study, the analysis of numerical convergence of FDM to the solution of diffusion equation is discussed. The analytical solution of diffusion equation is given by the separation of variables approach. Here, the result show the convergence of rate the numerical method is approximately approach 2. This result is in a good agreement with the spatial error from Taylor expansion of spatial second derivative.

scholarly journals A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Sachin Kumar ◽  
Jinde Cao ◽  
Xiaodi Li
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Research Work ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction

In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. For this, we developed a numerical scheme with the help of quasi-wavelets. The fractional term in the time direction is approximated by using the Crank–Nicolson scheme. The spatial term and the integral term present in integro reaction-diffusion are discretized and approximated with the help of quasi-wavelets. We study this model with Dirichlet boundary conditions. The discretization of these initial and boundary conditions is done with a different approach by the quasi-wavelet-based numerical method. The validity of this proposed method is tested by taking some numerical examples having an exact analytical solution. The accuracy of this method can be seen by error tables which we have drawn between the exact solution and the approximate solution. The effectiveness and validity can be seen by the graphs of the exact and numerical solutions. We conclude that this method has the desired accuracy and has a distinctive local property.

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