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The replacement of a Transcendent Function in a given interval by a polynomial function using Newton's Polynomial Interpolator

2023; Matthias-Grünewald-Verlag; Volume: 23; Issue: 2 Linguagem: Inglês

10.53660/clm-734-23a07

0010-5236

Gustavo Nogueira Dias, Washington Luiz Pedrosa da Silva, Afonso Costa da Silva Filho, Wagner Davy Lucas Barreto, Ricardo Daniel Soares Santos, José Carlos Barros de Souza Júnior, Katiane Pereira da Silva, Antônio Thiago Madeira Beirão, Alessandra Epifanio Rodrigues, Cássio Pinho dos Reis,

Iterative Methods for Nonlinear Equations

The work deals with the substitution of a transcendental function by a polynomial one, determined through Newton's Interpolator polynomial, in a certain interval, so that the characteristics in that space have a performance similar to that of the original function. Research enables numerous applications in the scientific field, as polynomial functions allow better predictability in the display of their graphics as well as in the entry of analytical points and results that are easy to manipulate and display. Some examples of application in the calculation of integrals were presented, presenting the calculations and obtaining the interpolating function. A comparative table was displayed with four transcendental functions, presenting equally acceptable results. The substitution of these functions in the integral calculation allows results with errors with a possibly acceptable margin in pre-established intervals.