Fisher Equation

This paper uses multi-country data for the period 1973–1994 to investigate five key equilibrium conditions in international finance—purchasing power parity, the Fisher equation, uncovered interest parity, and the equity-return analogues of the latter two. The results are largely consistent with theoretical expectations. Over the long run, purchasing power parity, uncovered interest parity and the Fisher effect prove to be rather

In this work, we propose several simple but accurate finite difference schemes to approximate the solutions of the nonlinear Fisher equation, which describes an interaction between logistic growth and diffusion process occurring in many biological and chemical phenomena. All schemes are based upon the time-splitting finite difference approximations. The operator splitting transforms the original problem into two subproblems: nonlinear logistic and linear diffusion, each with its own boundary conditions. The diffusion equation is solved by
three well-known stable and consistent methods while the logistic equation by a combination of method of lagging and a two-step approximation that is not only preserve positivity but also boundedness.
The new proposed schemes and the previous standard schemes are tested on a range of problems with analytical solutions. A comparison shows that the new schemes are simple, effective and very successful in solving the Fisher equation.

The numerical solution of second order ordinary differential equations with initial conditions is here approached by approximating each derivative by means of a set of finite difference schemes of high order. The stability properties of the obtained methods are discussed. Some numerical tests, reported to emphasize pros and cons of the approach, motivate possible choices on the use of these formulae. c © 2010 European Society of Computational Methods in Sciences and Engineering