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

Select Volume / Issue:

• Volume 11,Issue 1, Jan. 2023

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.

Full text: IJISM_985_FINAL.pdf [Bibtex]