A Derivative Free Hybrid Equation Solver by Alloying of the Conventional Methods

Authors

  • Amit Kumar Maheshwari Advanced Materials and Processes Research Institute (CSIR), Bhopal, India 462064

DOI:

https://doi.org/10.15415/mjis.2013.12009

Keywords:

Algebraic & Transcendental equations, Bisection method, Regula-Falsi method, Newton-Raphson method, Iteration Process, Derivative free methods

Abstract

This paper pronounces a modified numerical scheme to the conventional formula of Newton-Raphson for solving the nonlinear and transcendental equations especially
those which cannot be solved by the basic algebra. Finding the derivative of a function is difficult in some case of problems. The present formula is made with the target to
aloof the need of obtaining the derivative of the function. Comparative analysis shows that the present method is faster than Newton-Raphson method, Adomian method,
Rabolian method, Abbasbandy method, Basto method & Feng method. Iteration cost-effective parameters – number of iteration steps & the value of effective error is also
found to be minimum than these methods.

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References

Amit Kumar Maheshwari (2009), A fourth-order iterative method for solving nonlinear equations, Applied Mathematics and Computation, 211. 383–391 http://dx.doi.org/10.1016/j.amc.2009.01.047

Curtis F. Gerald, Patrick O. Wheatley (2004), Applied Numerical Analysis, Pearson Addition Wesley, New York, seventh edition.

Hildebrand F.B. (1982), Introduction to Numerical Analysis, Tata Mc. Graw, Hill Publishing Co. limited, New Delhi, Second Edition.

James M. Ortega, William G. Poole, Jr. (1981), An Introduction to Numerical Methods for Differential Equations, Pitman Publishing Inc., Massachussets.

Jishe Feng (2009), A New Two-step Method for Solving Nonlinear Equations, International Journal of Nonlinear Science, 8(1), 40-44. 10

Kreyszig Ervin (1972), Advanced Engineering Mathematics, Willey Eastern Limited, New Delhi, Third U.S. Edition.

Nasr-Al-Din Ide (2008), A new Hybrid iteration method for solving algebraic equations, Applied Mathematics and Computation, 195, 772–774. http://dx.doi.org/10.1016/j.amc.2007.05.022

Nasr-Al-Din Ide (2008), On modified Newton methods for solving a non-linear algebraic equation, Applied Mathematics, and Computation, 198, 138–142. http://dx.doi.org/10.1016/j.amc.2007.08.084

Richard L. Burden, J. Douglas Faires (2005), Numerical Analysis, Thomson Brooks/Cole, Eighth Edition.

Sidi Avram (2006), Unified Treatment of Regula Falsi, Newton-Raphson, Secant, and Steffensen Methods for Nonlinear Equations, Journal of Online Mathematics and Its Applications, 1-13.

Terry E. Shoup (1984), Applied Numerical methods for the microcomputer, Printice – Hall Inc., New Jersey.

Xing-Guo Luo (2005), A note on the new iteration method for solving an algebraic equation, Applied Mathematics, and Computation, 171 (2). 1177–1183, http://dx.doi.org/10.1016/j.amc.2005.01.124

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Published

2013-03-04

How to Cite

Amit Kumar Maheshwari. 2013. “A Derivative Free Hybrid Equation Solver by Alloying of the Conventional Methods”. Mathematical Journal of Interdisciplinary Sciences 1 (2):19-26. https://doi.org/10.15415/mjis.2013.12009.

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