Abstract
A general parabolic system of singularly perturbed linear equations of reaction-diffusion type is considered. The components of the solution exhibit overlapping layers. A numerical method with the Crank-Nicolson operator on a uniform mesh for time and classical finite difference operator on a Shishkin piecewise uniform mesh for space is constructed. It is proved that in the maximum norm, the numerical approximations obtained with this method are second order convergent in time and essentially second order convergent in space.
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References
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The authors thank the unknown referees for their suggestions and comments which helped us to get the paper in the present form.
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Victor, F., Miller, J.J.H., Sigamani, V. (2016). Convergence of the Crank-Nicolson Method for a Singularly Perturbed Parabolic Reaction-Diffusion System. In: Sigamani, V., Miller, J., Narasimhan, R., Mathiazhagan, P., Victor, F. (eds) Differential Equations and Numerical Analysis. Springer Proceedings in Mathematics & Statistics, vol 172. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3598-9_5
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DOI: https://doi.org/10.1007/978-81-322-3598-9_5
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