A new modified accelerated iterative scheme using amalgamation of fixed point and N-R method

Abstract

In this paper, a new two-step iterative scheme is developed by combining Newton-Raphson (N-R) method and fixed point iterative scheme. It has been seen that using first N-R method and then Fixed Point iterative scheme, the number of iterations required to converge to the solutions shows a significant decrement. Here, we have also discussed the efficiency of the scheme using some examples. Graphs are also drawn for error against number of iterations.

Subject Classification:

• (2010) 39B12
• 47J25
• 47J05
• 65N30

Keywords:

• Newton-Raphson method
• Two-step method
• Amalgamation
• Fixed-Point iterative scheme
• Number of iterations