Abstract
In this paper a boundary layer method is combined with an asymptotic expansion method to approximate the traveling wave solution of a nonlocal delayed reaction-diffusion model. In particular, assuming that the diffusion coefficients of the mature and immature populations are small, the wave solution is approximated in three steps. First, the model is reduced by considering the Dirac delta function as the kernel function of the integral term. Second, a boundary layer method is employed to approximate the wave solution of the reduced model. Third, using this result and the generalized Watson’s lemma, the wave solution of the general model is approximated. By considering various birth functions, the approximate wave solutions are numerically compared with the exact wave solutions.
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Acknowledgments
The author would like to thank Professor David E. Amundsen (Carleton University, Ottawa, Ontario, Canada) for his valuable suggestions and his role in strengthening the results of this paper. This work was partially supported by UMKC startup fund MO CODE # K0916043.
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Bani-Yaghoub, M. Approximating the traveling wavefront for a nonlocal delayed reaction-diffusion equation. J. Appl. Math. Comput. 53, 77–94 (2017). https://doi.org/10.1007/s12190-015-0958-7
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DOI: https://doi.org/10.1007/s12190-015-0958-7