Published July 8, 2022 | Version v1
Journal article Open

A New Technique for Finding Real Roots of Non-Linear Equations Using Arithmetic Mean Formula

  • 1. Department of Mathematics, Rajshahi University of Engineering and Technology, (RUET), Rajshahi-6204, Bangladesh

Description

The paper describes a new technique for finding real roots of both algebraic and transcendental non-linear equations using arithmetic mean formula. The new technique produces an iterative formula combining arithmetic mean formula and Newton-Rapson method. We have presented some numerical examples to compare the proficiency of proposed method together with results of known methods. The proposed method gives faster convergence and more accurate results than existing methods

Files

A New Technique for Finding.pdf

Files (545.9 kB)

Name Size Download all
md5:9f62b84645874489e42adca1975ac173
545.9 kB Preview Download

Additional details

References

  • Srinivasarao, T. (2019). A new root-finding algorithm using exponential series. Ural Mathematical Journal, 5(1 (8)), 83-90.
  • Chen, J. (2007). New modified regula falsi method for nonlinear equations. Applied mathematics and computation, 184(2), 965-971.
  • Noor, M. A., Noor, K. I., Khan, W. A., & Ahmad, F. (2006). On iterative methods for nonlinear equations. Applied mathematics and computation, 183(1), 128-133.
  • Noor, M. A., & Ahmad, F. (2006). Numerical comparison of iterative methods for solving nonlinear equations. Applied mathematics and computation, 180(1), 167-172.
  • Ehiwario, J. C., & Aghamie, S. O. (2014). Comparative study of bisection, Newton-Raphson and secant methods of root-finding problems. IOSR Journal of Engineering, 4(4), 01-07.
  • Hussain, S., Srivastav, V. K., & Thota, S. (2015). Assessment of interpolation methods for solving the real-life problem. Int. J. Math. Sci. Appl, 5(1), 91-95.
  • Thota, S., & Srivastav, V. K. (2018). Quadratically convergent algorithm for computing real root of non-linear transcendental equations. BMC research notes, 11(1), 1-6.
  • Thota, S., & Srivastav, V. K. (2014). Interpolation based hybrid algorithm for computing real root of non-linear transcendental functions. Int. J. Math. Comput. Research, 2(11), 729-735.
  • Abbasbandy, S., & Liao, S. J. (2008). A new modification of false position method based on homotopy analysis method. Applied Mathematics and Mechanics, 29(2), 223-228.
  • Srivastav, V. K., Thota, S., & Kumar, M. (2019). A new trigonometrical algorithm for computing real root of non-linear transcendental equations. International Journal of Applied and Computational Mathematics, 5(2), 1-8.