Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2021, 9(1), 17-21
DOI: 10.12691/tjant-9-1-3
Open AccessArticle

Delaying of Exponential Solution When Using Integral Factor Analysis Method to Solve Differential Equations

Kajisa T.1,

1Bioresources, Mie University, Tsu-city, Japan

Pub. Date: September 14, 2021

Cite this paper:
Kajisa T.. Delaying of Exponential Solution When Using Integral Factor Analysis Method to Solve Differential Equations. Turkish Journal of Analysis and Number Theory. 2021; 9(1):17-21. doi: 10.12691/tjant-9-1-3


It was confirmed that the results given by the integral factor method showed the delaying of response in the numerical experiments using the advection-diffusion equation. However, the exponential solutions given by the integral factor method were not very smooth compared to the analytically correct solution. On the other hand, a delay in the exponential solution was clearly found for an increasing time increment. Therefore it is important to make the time increment shorter step by step, to check the delaying when applying this integral factor method. It would be expected that the exponential solution given by the integral factor analysis method shown here would have the same expression. That would mean that this method had great potential and could be widely used.

integral factor method exponential Taylor method advection–diffusion equation

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[1]  Kajisa T., Ermolin Y., The stabilized answer of diffusion equation for unsteady 3-D unsaturated subsurface flow analysis, December 2000, International Agricultural Engineering Conference, Asian Institute of Technology, Thailand, 2000. https://www.researchgate.net/publication/343787565.
[2]  Inan B., A.R. Bahadir, Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods, Pramana, 2013. https://link.springer.com/article/10.1007/s12043-013-0599-z.
[3]  Bhattacharya M.C., Int. J. Numer. Methods Eng. 21, 239 (1985).
[4]  Koskela A. and Ostermann A., Exponential Taylor methods: Analysis and implementation, A Ostermann - Computers & Mathematics with Applications, 65, 487-499, 2013.
[5]  Ayinde S.O., Ibijola E.A., A new Numerical Method for Solving First Order Differential Equtions, American journal of Applied Mathematics and Statistics, vol. 3, no. 4, 2015: 156-160.
[6]  Savović S., Djordjevich A., Explicit finite difference solution of for contaminant transport problems with constant and oscillating boundary conditions, Thermal Science, May 2020.
[7]  Kitagawa M., Murakami Y., Stable and highly accurate numerical solution of nonlinear wave equations, New progress in research on nonlinear wave phenomena, Research Institute for Mathematical Sciences, 1800: 226-235, 2012 (in Japanese).