Fractional Newton's method

• Grant number: 19/10619-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2019
• End date: December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Eliana Contharteze Grigoletto
• Grantee: Giovana Lanza Okada
• Host 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.