Using ASCII text files in post-fix notation (reverse Polish) to define mathematical models and systems of differential equations for simulation and non-linear regression

Abstract

We discuss current methods for supplying equations in ASCII text form to executables for simulation or fitting, then we define a technique using stack notation that has many advantages over traditional approaches to this problem. Simulations are described to compare the cpu time consumed for function evaluation when the models are supplied as object code in dynamic-link libraries, and when they are supplied as ASCII text files in post-fix notation, otherwise known as last-in-first-out or reverse Polish. It is concluded that this new method is extremely convenient; it can be easily extended to include loops for numerical integration, special function evaluation or root finding; it can be optimized by the user for execution speed; and the cpu overhead when the models are involved in regression are minimal.