Jarratt and Jarratt-variant families of iterative schemes for scalar and system of nonlinear equations

This manuscript put forward two new generalized families of Jarratt’s iterative schemes for deciding the solution of scalar and systems of nonlinear equations. The schemes involve weight functions that are based on a bi-variate rational approximation polynomial of degree two in both its numerator and denominator. The convergence study conducted on the schemes indicated that they have convergence order (CO) four in scalar space and retain the same number of CO in vector space. The numerical experiments conducted on the schemes when used to decide the solutions of some real-life nonlinear models, show that they are good challengers of some well-known and robust existing iterative schemes.

Keywords:

Jarratt scheme , Iterative scheme , Rational approximation polynomial , Nonlinear equation , Systems of nonlinear equations