A New Iterative Method of Solution of Nonlinear Equations Derived from Simpson and Trapezoidal Quadrature Rules

Hits: 427
Select Volume / Issue:
Year:
2023
Type of Publication:
Article
Keywords:
Quadrature Rules, Nonlinear Equations, Iterative Methods, Number of Iterations, Run Time
Authors:
Stephen B. Twum; Yahaya L. Remembrance
Journal:
IJISM
Volume:
11
Number:
1
Pages:
10-19
Month:
January
ISSN:
2347-9051
Abstract:
Many problems in Engineering, Computer Science, and Applied Mathematics among other fields lead to the solution of nonlinear equations. Nontrivial cases of such equations can only be solved iteratively. Development of efficient and effective iterative methods therefore is very important, and can impact positively the task of finding numerical solutions of many real-world problems. This paper is devoted to developing a new and efficient iterative method for solving nonlinear equations. The new method is derived from a weighted combination of the Simpson and Trapezoidal schemes, which are derivatives of the Newton-Cotes quadrature rules of integration, in conjunction with a new iterative method reported in the literature. The newly developed method was shown to converge and its performance compared with Newton’s and a newer method, using several benchmark problems, with their run-time, the number of iterations before converging, and the size of the error of the approximated solutions as the indicators. The Results showed that the newly developed method performed as good as the classical Newton’s method and the leading method in some of the cases and better than them in many of the cases. This provides grounds for confidence in the newly developed method and provides prospects for further refinement in future work.

About Us

Our Journals

IJECCE
International Journal of Electronics Communication and Computer Engineering
ISSN(Online): 2249 - 071X
ISSN (Print) : 2278 – 4209
www.ijecce.org
Submissions open
IJAIR
International Journal of Agriculture Innovations and Research (ISSN(Online) : 2319 – 1473)
www.ijair.org
Submissions open
IJISM
International Journal of Innovation in Science and Mathematics
ISSN : 2347 – 9051
www.ijism.org
Submissions open
IJEIR
International Journal of Engineering Innovations and Research
ISSN(Online) : 2277 – 5668
www.ijeir.org
Submissions are open.

IJAIM
International Journal of Artificial Intelligence and Mechatronics (ISSN(Online) : 2320 – 5121)
www.ijaim.org
Submissions open
IJRAS
International Journal of Research in Agricultural Sciences
www.ijras.org
Submissions open

Indexed By:

 width= width= width= width= width=