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Fractional Newton's method

Grant number: 19/10619-4
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): August 01, 2019
Effective date (End): December 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computational Mathematics
Principal Investigator:Eliana Contharteze Grigoletto
Grantee:Giovana Lanza Okada
Home Institution: Faculdade de Ciências Agronômicas (FCA). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil

Abstract

Newton's method is a very useful iterative method for solving nonlinear equations F(x)=0 and converges rapidly if the x0 values are good starting values. We intend to study some numerical examples of the fractional Newton's method for solving nonlinear equations. In the fractional version of the classical method, we can use fractional derivatives of different orders in the Jacobian matrix. We intend to compare the fractional Newton's method with the classical iteration method from the point of view of the total CPU time and in terms of the number of iteration steps.