Algorithms for Solving the Catch Equation Forward and Backward in Time

Abstract

Approximate solutions to the catch equation for the fishing mortality rate both forward and backward in time are obtained with an application of the diagonal Padé approximation of degree four to the exponential function. In either case the resulting approximation as well as Pope's estimate are shown to serve quite well as starting values for Newton's Method which is used to obtain a numerical solution of the catch equation. Convergence criteria for Newton's Method are discussed in each setting.Key words: catch equation, Newton's method, Padé approximation, Pope's estimate