Numerical analysis of the Caughley model from ecology∗,†

This paper deals with numerical analysis of a reaction diffusion model from mathematical ecology posed in an unbounded spatial domain. For numerical simulations we replace the original system with an equivalent one posed in a bounded domain. This is done by means of an algebraic map in conjunction with a spectral method. For the semidiscretization in time we use an exponential time differencing scheme, the resulting scheme is explicit both in space and time. Improved error estimates are derived and the computational efficiency of the algorithm is considered. Finally, we present several numerical simulations which are useful for making pertinent biological deductions. AMS subject classifications: 65M70, 65M15, 92D40