Keywords:-
Keywords:
Transcendental equations; Newton-Raphson method; quadratic equation; Taylor’s series
Article Content:-
Abstract
Newton-Raphson method and iteration method are widely used to solve non-algebraic or transcendental equation. In this paper we use first three terms of Taylor’s series to find the equivalent quadratic equation. Solving this quadratic equation we can easily find an iterative formula for the solution which gives better approximation than that of NewtonRaphson method. Here we present comparison of the roots and its convergency in geometric view.
References:-
References
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2. Mostak Ahmed and Samir Kumar Bhowmik − Solution of Transcendental Equation Using Clamped Cubic Spline, Dhaka University Journal of Science (ISSN: 1022-2502), Accepted for Publication, 2012.
3. Mostak Ahmed and M. Alamgir Hossain − Transcendental Equation in Quadratic Form and Its Solution, Bangladesh Journal of Scientific and Industrial Research (ISSN:
0304-9809), Vol.: 47(2), 239-242, 2012.
4. L.E Bateson, M.A Kelmanson, C Knudsen – Solution of a transcendental eigenvalue problem via interval analysis, Computers & Mathematics with Applications, Vol: 38(7–8), 133–142, October 1999.
5. James L. Howland, Rémi Vaillancourt – Selective solutions to transcendental equations, Computers & Mathematics with Applications, Vol: 22(9), 61–76,
1991
6. E. Balagurusamy, Numerical Method, Thirteenth Reprint, 2004.
7. R.L. Burden, J. Douglas Faires, Numerical Analysis, Seventh Ed.,
Thomson Learning, 2001.
8. S.S. Sastry, Introductory Methods of Numerical Analysis, Third Ed., Prentice-Hall of India Private Limited, 1999
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Ahmed, M., & Ghosh, B. P. (2013). Root of a Transcendental Equation: Geometric View of Taylor’s Approximation. International Journal Of Mathematics And Computer Research, 1(05), 138-144. Retrieved from https://ijmcr.in/index.php/ijmcr/article/view/299