An improved numerical method to find parameters using experimental data

✍ Scribed by Ihtzaz Qamar; S. Wilayat Husain

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 508 KB
• Volume: 36
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620361612

✦ Synopsis

In this paper we describe a numerical method to determine adjustable parameters in a mathematical model using experimental data. This is basically an improvement over our earlier method which was based on the idea that the area under the experimental curve must be equal to the integral of the function used. The improvement used is the addition of an area correction factor which estimates the necessary difference that must exist between the numerically evaluated and the true area. This correction surprisingly eliminates the use of integral with the result that the two areas being equaliLed are both numerically evaluated, one using the experimental data points and the other using the fitted function values. It is shown that the application of the area correction factor significantly improves the accuracy of the adjusted parameters. The method has been compared with the well-known method of least squares for few selected cases involving variety of functions. It is seen that our method shows convergence for a wider range of initial guesses as compared to the method of least squares. The superiority of our method becomes evident when more than two non-linear parameters are involved.