Title of article :
An iterative method based on the average quadrature formula
Author/Authors :
Singh ، Tusar Department of Mathematics - Siksha O Anusandhan University , Behera ، Dwiti Krushna Department of Mathematics - Ravenshaw University , Ahmed ، Shno Othman Department of Computer - College of Science - Salahaddin University-Erbil , Saeed ، Rostam Kareem Department of Mathematics - College of Science - Salahaddin University-Erbil
Abstract :
In our research, a new third-order iterative method has been introduced. This method involves the creation of a new quadrature formula by averaging Simpson’s 1/3 rd and Trapezoidal rules. The newly developed quadrature formula is then used to establish the new iterative scheme, which modifies the Newton-Raphson method. It has been demonstrated that the new iterative technique exhibits a convergence order of 3. Finally, examples have been provided to illustrate the effectiveness of the new process. The results indicate that the new approach finds the root of the nonlinear equation in fewer iterations compared to other methods, suggesting the potential superiority of our newly developed scheme.
Keywords :
Trapezoidal rule , Simpson s 1 , 3rd , Newton’s method , Order of convergence , Iterative method
Journal title :
Computational Algorithms and Numerical Dimensions (CAND)
Journal title :
Computational Algorithms and Numerical Dimensions (CAND)
