A nonlinear least squares program based on differential equations, MULTI (RUNGE), for microcomputers.

Abstract

A nonlinear least squares program based on first-order simultaneous differential equations, MULTI (RUNGE), for personal computers was developed. Four algorithms, i.e. the classical Gauss-Newton method, the damping Gauss-Newton method, the modified Marquardt method and the simplex method can be used for the nonlinear curve fitting in MULTI (RUNGE). The differential equations and the initial conditions which are voluntarily defined by the user are numerically solved by the Runge-Kutta-Gill method and the numerically integrated solutions are fitted to the observed data points by the iterative least squares algorithms. MULTI (RUNGE) can be executed on many personal computers without any modification, because this program is written in the Microsoft minimum BASIC commands alone. The dimensions of differential equations, the number of parameters to evaluate and the number of experimental data points are restricted only by the available memory in computers and by the computing time.