EULER AND TAYLOR POLYNOMIALS METHOD FOR SOLVING VOLTERRA TYPE INTEGRO DIFFERENTIAL EQUATIONS WITH NONLINEAR TERMS
Küçük Resim Yok
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Editura Bibliotheca-Bibliotheca Publ House
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this study, the first order nonlinear Volterra type integro-differential equations are used in order to identify approximate solutions concerning Euler polynomials of a matrix method based on collocation points. This method converts the mentioned nonlinear integro-differential equation into the matrix equation with the utilization of Euler polynomials along with collocation points. The matrix equation is a system of nonlinear algebraic equations with the unknown Euler coefficients. Additionally, this approach provides analytic solutions, if the exact solutions are polynomials. Furthermore, some illustrative examples are presented with the aid of an error estimation by using the Mean-Value Theorem and residual functions. The obtained results show that the developed method is efficient and simple enough to be applied. And also, convergence of the solutions of the problems were examined. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB.
Açıklama
Anahtar Kelimeler
Euler and Taylor polynomials, collocation points, residual error analysis, matrix method, nonlinear terms, Volterra integro differential equation
Kaynak
Journal Of Science And Arts
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
Sayı
2
