Fractional Step Runge-Kutta Methods for the Resolution of Two Dimensional Time Dependent Coefficient Convection-Diffusion Problems

2001 ◽  
pp. 133-143
Author(s):  
B. Bujanda ◽  
J. C. Jorge
Keyword(s):  
Time Dependent ◽  
Fractional Step ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Runge Kutta ◽  
Diffusion Problems

An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems

2016 ◽  
Vol 20 (5) ◽  
pp. 1340-1358 ◽  
Author(s):  
Yanping Chen ◽  
Li-Bin Liu
Keyword(s):  
Numerical Solution ◽  
Time Derivative ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Time Dependent ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Monitor Function ◽  
Backward Euler ◽  
Diffusion Problems

AbstractIn this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε-uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.

scholarly journals Analytical and approximate solution of two-dimensional convection-diffusion problems

2020 ◽  
Vol 10 (1) ◽  
pp. 73-77 ◽  
Author(s):  
Hatıra Günerhan
Keyword(s):  
Approximate Solution ◽  
Research Work ◽  
Convergent Series ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Transform Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Differential Transform ◽  
Diffusion Problems

In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work.

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