Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations
Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that...
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| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124002882 |
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| author | Farooq Ahmed Shah Muhammad Waseem Alexey Mikhaylov Gabor Pinter |
| author_facet | Farooq Ahmed Shah Muhammad Waseem Alexey Mikhaylov Gabor Pinter |
| author_sort | Farooq Ahmed Shah |
| collection | DOAJ |
| description | Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus. |
| format | Article |
| id | doaj-art-ba924a7140fe48579398c5f1826fb530 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-ba924a7140fe48579398c5f1826fb5302024-12-13T11:05:30ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100902Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equationsFarooq Ahmed Shah0Muhammad Waseem1Alexey Mikhaylov2Gabor Pinter3COMSATS University Islamabad, Attock Campus, PakistanCOMSATS University Islamabad, Vehari Campus, PakistanFinancial University under the Government of the Russian Federation, Moscow, RussiaFaculty of Engineering, Soos Erno, Research and Development Center, Renewable Energy Research Group, University of Pannonia, Veszprem, 8200, Hungary; Corresponding author.Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.http://www.sciencedirect.com/science/article/pii/S266681812400288211a0565h20,58c3090C30 |
| spellingShingle | Farooq Ahmed Shah Muhammad Waseem Alexey Mikhaylov Gabor Pinter Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations Partial Differential Equations in Applied Mathematics 11a05 65h20,58c30 90C30 |
| title | Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| title_full | Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| title_fullStr | Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| title_full_unstemmed | Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| title_short | Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| title_sort | modification of adomian decomposition technique in multiplicative calculus and application for nonlinear equations |
| topic | 11a05 65h20,58c30 90C30 |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124002882 |
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