Abstract
A finite element solution of the Fisher’s equation based on the Galerkin method whose weight and shape functions are exponential B-splines are constructed. A travelling wave propagation having analytical solution is studied to compare results in term of the maximum error norm. Both steep and flat initial disturbances are shown to see effects of the diffusion and reaction, form two progressive waves propagating in both opposite directions at long run of the algorithm. The shape and the speed of the long term progressive waves are observed not to depend on the initial disturbance. Graphical solutions and tabulated values are presented to show efficiency of the method.
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Acknowledgements
All of the authors are grateful to The Scientific and Technological Research Council of Turkey for financial support for the project (113F394). This paper was presented at International Congress on Fundamental and Applied Sciences 2016 (ICFAS2016) in Istanbul.
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Zorsahin Gorgulu, M., Dag, I. Exponential B-splines Galerkin Method for the Numerical Solution of the Fisher’s Equation. Iran J Sci Technol Trans Sci 42, 2189–2198 (2018). https://doi.org/10.1007/s40995-017-0403-x
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DOI: https://doi.org/10.1007/s40995-017-0403-x