On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term

dc.contributor.authorAgbavon, Koffi Messan
dc.contributor.authorAppadu, A. Rao
dc.contributor.authorKhumalo, M.
dc.contributor.emailrao.appadu@up.ac.zaen_ZA
dc.date.accessioned2020-06-05T06:06:59Z
dc.date.available2020-06-05T06:06:59Z
dc.date.issued2019-04-18
dc.description.abstractLi et al. (SIAM J. Sci. Comput. 20:719–738, 1998) used the moving mesh partial differential equation (MMPDE) to solve a scaled Fisher’s equation and the initial condition consisting of an exponential function. The results obtained are not accurate because MMPDE is based on a familiar arc-length or curvature monitor function. Qiu and Sloan (J. Comput. Phys. 146:726–746, 1998) constructed a suitable monitor function called modified monitor function and used it with the moving mesh differential algebraic equation (MMDAE) method to solve the same problem of scaled Fisher’s equation and obtained better results. In this work, we use the forward in time central space (FTCS) scheme and the nonstandard finite difference (NSFD) scheme, and we find that the temporal step size must be very small to obtain accurate results. This causes the computational time to be long if the domain is large. We use two techniques to modify these two schemes either by introducing artificial viscosity or using the approach of Ruxun et al. (Int. J. Numer. Methods Fluids 31:523–533, 1999). These techniques are efficient and give accurate results with a larger temporal step size. We prove that these four methods are consistent for partial differential equations, and we also obtain the region of stability.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianam2020en_ZA
dc.description.sponsorshipThe South African DST/NRF SARChI on Mathematical Models and Methods in Bioengineering and Biosciences (M3B2).en_ZA
dc.identifier.citationAgbavon, K.M., Appadu, A.R. & Khumalo, M. 2019, 'On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term', Advances in Difference Equations, vol. 2019, art. 146, pp. 1-33.en_ZA
dc.identifier.issn1687-1839 (print)
dc.identifier.issn1687-1847 (online)
dc.identifier.other10.1186/s13662-019-2080-x
dc.identifier.urihttp://hdl.handle.net/2263/74871
dc.language.isoenen_ZA
dc.publisherSpringerOpenen_ZA
dc.rights© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.en_ZA
dc.subjectFisher’s equationen_ZA
dc.subjectMoving mesh methoden_ZA
dc.subjectArtificial viscosityen_ZA
dc.subjectMoving mesh partial differential equation (MMPDE)en_ZA
dc.subjectMoving mesh differential algebraic equation (MMDAE)en_ZA
dc.subjectModified monitor functionen_ZA
dc.subjectForward in time central space (FTCS)en_ZA
dc.subjectNonstandard finite difference (NSFD)en_ZA
dc.titleOn the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction termen_ZA
dc.typeArticleen_ZA

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Agbavon_On_2019.pdf
Size:
2.79 MB
Format:
Adobe Portable Document Format
Description:
Article

License bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
license.txt
Size:
1.75 KB
Format:
Item-specific license agreed upon to submission
Description: