Generalized Laguerre spectral method for Fisher's equation on a semi-infinite interval

Abstract

In this paper, we propose a generalized Laguerre spectral method for Fisher's-type equation with inhomogeneous boundary conditions on a semi-infinite interval. By reformulating the equation with suitable functional transform, it is shown that the generalized Laguerre approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the generalized Laguerre approximations to the transformed equation is developed and implemented. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.

Keywords:

• Fisher's equations
• generalized Laguerre spectral method
• inhomogeneous boundary conditions

2000 AMS Subject Classifications::

• 65M70
• 41A30
• 35K55
• 35B30
• 35R15

Acknowledgements

The work of this author is supported in part by NSF of China N.11371123 and N.11171227, Fund of Henan Education Commission N.2011B110014 and N.14B11021 and The Doctor Fund of Henan University of Science and Technology N.09001263.