Applicable Analysis and Discrete Mathematics 2013 Volume 7, Issue 2, Pages: 390-403
https://doi.org/10.2298/AADM130725016S
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An efficient derivative free iterative method for solving systems of nonlinear equations
Sharma Janak Raj (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India)
Arora Himani (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India)
We present a derivative free method of fourth order convergence for solving
systems of nonlinear equations. The method consists of two steps of which
first step is the well-known Traub's method. First-order divided difference
operator for functions of several variables and direct computation by
Taylor's expansion are used to prove the local convergence order.
Computational efficiency of new method in its general form is discussed and
is compared with existing methods of similar nature. It is proved that for
large systems the new method is more efficient. Some numerical tests are
performed to compare proposed method with existing methods and to confirm the
theoretical results.
Keywords: systems of nonlinear equations, iterative methods, derivative free methods, order of convergence, computational efficiency