A Multiplicative Calculus Approach to Solve Applied Nonlinear Models
Problems such as population growth, continuous stirred tank reactor (CSTR), and ideal gas have been studied over the last four decades in the fields of medical science, engineering, and applied science, respectively. Some of the main motivations were to understand the pattern of such issues and how...
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| Format: | Article |
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MDPI AG
2023-02-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/28/2/28 |
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| author | Gurjeet Singh Sonia Bhalla Ramandeep Behl |
| author_facet | Gurjeet Singh Sonia Bhalla Ramandeep Behl |
| author_sort | Gurjeet Singh |
| collection | DOAJ |
| description | Problems such as population growth, continuous stirred tank reactor (CSTR), and ideal gas have been studied over the last four decades in the fields of medical science, engineering, and applied science, respectively. Some of the main motivations were to understand the pattern of such issues and how to obtain the solution to them. With the help of applied mathematics, these problems can be converted or modeled by nonlinear expressions with similar properties. Then, the required solution can be obtained by means of iterative techniques. In this manuscript, we propose a new iterative scheme for computing multiple roots (without prior knowledge of multiplicity <i>m</i>) based on multiplicative calculus rather than standard calculus. The structure of our scheme stands on the well-known Schröder method and also retains the same convergence order. Some numerical examples are tested to find the roots of nonlinear equations, and results are found to be competent compared with ordinary derivative methods. Finally, the new scheme is also analyzed by the basin of attractions that also supports the theoretical aspects. |
| first_indexed | 2024-03-11T04:46:48Z |
| format | Article |
| id | doaj.art-75add45d87e3420b8aeddc91d18732c0 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-11T04:46:48Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-75add45d87e3420b8aeddc91d18732c02023-11-17T20:19:16ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472023-02-012822810.3390/mca28020028A Multiplicative Calculus Approach to Solve Applied Nonlinear ModelsGurjeet Singh0Sonia Bhalla1Ramandeep Behl2Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, IndiaDepartment of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, IndiaMathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaProblems such as population growth, continuous stirred tank reactor (CSTR), and ideal gas have been studied over the last four decades in the fields of medical science, engineering, and applied science, respectively. Some of the main motivations were to understand the pattern of such issues and how to obtain the solution to them. With the help of applied mathematics, these problems can be converted or modeled by nonlinear expressions with similar properties. Then, the required solution can be obtained by means of iterative techniques. In this manuscript, we propose a new iterative scheme for computing multiple roots (without prior knowledge of multiplicity <i>m</i>) based on multiplicative calculus rather than standard calculus. The structure of our scheme stands on the well-known Schröder method and also retains the same convergence order. Some numerical examples are tested to find the roots of nonlinear equations, and results are found to be competent compared with ordinary derivative methods. Finally, the new scheme is also analyzed by the basin of attractions that also supports the theoretical aspects.https://www.mdpi.com/2297-8747/28/2/28multiplicative derivativenonlinear equationsSchröder methodorder of convergence |
| spellingShingle | Gurjeet Singh Sonia Bhalla Ramandeep Behl A Multiplicative Calculus Approach to Solve Applied Nonlinear Models Mathematical and Computational Applications multiplicative derivative nonlinear equations Schröder method order of convergence |
| title | A Multiplicative Calculus Approach to Solve Applied Nonlinear Models |
| title_full | A Multiplicative Calculus Approach to Solve Applied Nonlinear Models |
| title_fullStr | A Multiplicative Calculus Approach to Solve Applied Nonlinear Models |
| title_full_unstemmed | A Multiplicative Calculus Approach to Solve Applied Nonlinear Models |
| title_short | A Multiplicative Calculus Approach to Solve Applied Nonlinear Models |
| title_sort | multiplicative calculus approach to solve applied nonlinear models |
| topic | multiplicative derivative nonlinear equations Schröder method order of convergence |
| url | https://www.mdpi.com/2297-8747/28/2/28 |
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