Some Real-Life Applications of a Newly Constructed Derivative Free Iterative Scheme
| Autor: | Somayeh Sharifi, Massimiliano Ferrara, Ramandeep Behl, Mehdi Salimi, Samaher Khalaf Alharbi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Scheme (programming language)
Steffensen’s method Physics and Astronomy (miscellaneous) Computer science Iterative method General Mathematics computational convergence order 010103 numerical & computational mathematics Derivative 01 natural sciences Steffensen's method Simple (abstract algebra) Convergence (routing) Computer Science (miscellaneous) Applied mathematics 0101 mathematics basins of attraction computer.programming_language lcsh:Mathematics 010102 general mathematics scalar equations lcsh:QA1-939 Transformation (function) Chemistry (miscellaneous) Constant (mathematics) computer |
| Zdroj: | Symmetry, Vol 11, Iss 2, p 239 (2019) Symmetry Volume 11 Issue 2 |
| ISSN: | 2073-8994 |
| Popis: | In this study, we present a new higher-order scheme without memory for simple zeros which has two major advantages. The first one is that each member of our scheme is derivative free and the second one is that the present scheme is capable of producing many new optimal family of eighth-order methods from every 4-order optimal derivative free scheme (available in the literature) whose first substep employs a Steffensen or a Steffensen-like method. In addition, the theoretical and computational properties of the present scheme are fully investigated along with the main theorem, which demonstrates the convergence order and asymptotic error constant. Moreover, the effectiveness of our scheme is tested on several real-life problems like Van der Waal&rsquo s, fractional transformation in a chemical reactor, chemical engineering, adiabatic flame temperature, etc. In comparison with the existing robust techniques, the iterative methods in the new family perform better in the considered test examples. The study of dynamics on the proposed iterative methods also confirms this fact via basins of attraction applied to a number of test functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|