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

Area of Science:

• Computational chemistry
• Mathematical modeling
• Scientific computing

Background:

• Nonlinear curve fitting is essential for analyzing experimental data in various scientific fields.
• Existing methods often require specialized software or significant computational resources.
• A need exists for accessible and versatile tools for fitting data to differential equations.

Purpose of the Study:

• To develop a user-friendly nonlinear least squares program for personal computers.
• To implement multiple algorithms for robust nonlinear curve fitting.
• To enable the analysis of data described by first-order simultaneous differential equations.

Main Methods:

• The MULTI (RUNGE) program utilizes the Runge-Kutta-Gill method for numerical integration of differential equations.
• It incorporates four iterative least squares algorithms: Gauss-Newton, damped Gauss-Newton, Marquardt, and simplex methods.
• The program is written in Microsoft minimum BASIC for broad personal computer compatibility.

Main Results:

• MULTI (RUNGE) successfully performs nonlinear curve fitting using user-defined differential equations and initial conditions.
• The program's flexibility allows for the evaluation of multiple parameters and fitting to various experimental data points.
• Its compatibility across different personal computers enhances accessibility for researchers.

Conclusions:

• MULTI (RUNGE) provides an accessible and versatile tool for nonlinear data fitting using differential equations on personal computers.
• The program's implementation of multiple algorithms enhances its applicability to diverse scientific problems.
• Further development could explore optimization for larger datasets and more complex models.