Construction of iterative adaptive methods with memory with 100% improvement of convergence order
Abstract
An efficient family of the recursive methods of adaptive is proposed for
solving nonlinear equations, is developed such that all previous information are applied. These methods have reached the maximum degree of convergence improvement of 100%, and also have an efficiency index of 2. Three families have been examined from Steffensen-Like single, two, and three-step methods that have used 2, 3 and 4 parameters respectively. Numerical comparisons are made with other existing methods one-, two-, three-, and four-point to show the performance of the convergence speed of the proposed method and confirm theoretical results.
solving nonlinear equations, is developed such that all previous information are applied. These methods have reached the maximum degree of convergence improvement of 100%, and also have an efficiency index of 2. Three families have been examined from Steffensen-Like single, two, and three-step methods that have used 2, 3 and 4 parameters respectively. Numerical comparisons are made with other existing methods one-, two-, three-, and four-point to show the performance of the convergence speed of the proposed method and confirm theoretical results.
Keywords
Adaptive method with memory; Accelerator parameter; Nonlinear equations; Newton's interpolatory polynomial; Order convergence
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