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All Journal Journal of the Indonesian Mathematical Society Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Ayunda Putri
Universitas Riau
Computer Science & IT Mathematics

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Arithmetic Mean Derivative-Based Quartet Midpoint Rule Rike Marjulisa; Ayunda Putri
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.22961

Abstract

A definite integral that is difficult to solve analytically can be calculated using the numerical integration methods. The midpoint rule is a prominent rule for approximating definite integrals. This article discusses a version of the quartet midpoint rule that includes the derivative of the arithmetic mean . The proposed rule increases precision over the previous rules. Furthermore, the error term is obtained by using the concept of precision between quadrature and exact values. Finally, the proposed rule is more effective than the present rule, according to numerical simulation results.
A NEW THREE- STEP DERIVATIVE FREE ITERATIVE METHOD AND ITS DYNAMICS Syamsudhuha Syamsudhuha; M Imran; Ayunda Putri; Leli Deswita; Riski Amelia
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1533.361-373

Abstract

A new free derivative iterative method is presented in this article. The method is developed by combining Newton’s method and Euler’s method. Deriva- tives in this method are approximated by forward difference, hyperbola and divided difference. The order of convergence is proven analytically to be of sixth order. Numerical results exhibit that the new method is comparable to other methods. Basins of attraction are also provided to support the proposed method.
Co-Authors Leli Deswita M. Imran Rike Marjulisa Riski Amelia Syamsudhuha Syamsudhuha