Determination of the Finite Differences Method coefficients

• Autor(a) principal: Silva, Luciano Cesario da
• Data de Publicação: 2023
• Outros Autores: Nascimento Junior, Paulo Cavalcante do
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Research, Society and Development
• Texto Completo: https://rsdjournal.org/index.php/rsd/article/view/39946
• topic: Determination of coefficients; Ordinary Differential Equations; Finite Difference Method; Numerical method.; Determinación de coeficientes; Ecuaciones Diferenciales Ordinarias; Método de Diferencias Finitas; Método numérico.; Determinação de coeficientes; Equações Diferenciais Ordinárias; Método das Diferenças Finitas; Método numérico.

This article aims to present a procedure to determine of the Finite Difference Method (FDM) coefficients. The approach contained in the work consists of approximating derivatives of different orders from the first terms of the Taylor Series, obtaining coefficients that are used in the construction of the Finite Difference Equation (FDE), which is used to approximate the solution of a Differential Equation Ordinary (ODE). For the derivatives of a function, a process was developed that takes as a basis the cases of the first derivatives of a function and generalizes to the derivative of nth order. From them it is possible to expand the numerical method of study to approach the solution of an ODE of any order. To exemplify the applications of FDM, contemporary physical problems that fall into integrated and compatible with approximate solutions were made, where, in each case, it was necessary to build an FDE associated with the ODE and solve the linear system generated by this FDE. In addition, for comparison purposes, the exact values of the solutions were presented to verify the difference between the approximate solution and the exact solution.