A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX

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LOTFI T.; ASSARI P.

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Journal: INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION Year:2014 | Volume:4 | Issue:3 Page(s): 277-288

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Information Journal Paper

Title

A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX

Author(s)

LOTFI T. | ASSARI P. | Issue Writer Certificate

Keywords

NONLINEAR EQUATION

WITH MEMORY METHOD

R-ORDER OF CONVERGENCE

SELF-ACCELERATING PARAMETER

Abstract

It is attempted to extend a two-step without memory method to its with mem- ory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solv- ing NONLINEAR EQUATIONs. Eventually, we obtain a new class of methods by employing a self- accelerating parameter calculated in each iterative step applying only information from the current and the previous iterations, de ning a with memory class.Although these improvements are achieved without any additional function evaluations, the R-ORDER OF CONVERGENCE are boosted from 4 to 5.24 and 6, respectively, and it is demonstrated that the proposed with memory classes provide a very high computational efficiency.Numerical examples are put forward and the performances are compared with the basic two- step without memory methods.

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ON A NOVEL OPTIMAL QUARTICALLY CLASS OF METHODS

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APA: Copy

LOTFI, T., & ASSARI, P.. (2014). A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, 4(3), 277-288. SID. https://sid.ir/paper/328322/en

Vancouver: Copy

LOTFI T., ASSARI P.. A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION[Internet]. 2014;4(3):277-288. Available from: https://sid.ir/paper/328322/en

IEEE: Copy

T. LOTFI, and P. ASSARI, “A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX,” INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, vol. 4, no. 3, pp. 277–288, 2014, [Online]. Available: https://sid.ir/paper/328322/en

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