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Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi
- Source :
- Journal of Mathematics, Vol 2016 (2016)
- Publication Year :
- 2016
- Publisher :
- Hindawi Limited, 2016.
-
Abstract
- In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.
- Subjects :
- Article Subject
lcsh:Mathematics
General Mathematics
Science and engineering
Numerical analysis
Multiplicative function
Mathematical analysis
Numerical methods for ordinary differential equations
02 engineering and technology
lcsh:QA1-939
01 natural sciences
010101 applied mathematics
Nonlinear system
Range (mathematics)
Rate of convergence
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
020201 artificial intelligence & image processing
0101 mathematics
Root-finding algorithm
Mathematics
Subjects
Details
- ISSN :
- 23144785 and 23144629
- Volume :
- 2016
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....5335afa2c296ad30d5b890ed025f2340