Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators
This research looked at nonlinear ordinary differential equations with global differential operators and the Dirac-delta and exponential decay kernels. A recently developed numerical approach based on the repetitive use of the well-known midpoint quadrature approximation. Although no theoretical ana...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011682 |
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| author | Abdon Atangana Seda Igret Araz |
| author_facet | Abdon Atangana Seda Igret Araz |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | This research looked at nonlinear ordinary differential equations with global differential operators and the Dirac-delta and exponential decay kernels. A recently developed numerical approach based on the repetitive use of the well-known midpoint quadrature approximation. Although no theoretical analysis was offered, the method was applied to solve several nonlinear equations in chaos and epidemiology. The observed findings demonstrate the effect of the chosen function gt, for example, a simple SIR model produced chaotic and crossover behaviors. |
| format | Article |
| id | doaj-art-c37a4b76d8104277a48345b8155cff40 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-c37a4b76d8104277a48345b8155cff402025-01-18T05:03:33ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111374384Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operatorsAbdon Atangana0Seda Igret Araz1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 70800, Ostrava-Poruba, Czech Republic; Corresponding author at: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.Department of Mathematic Education, Faculty of Education, Siirt University, Siirt 56100, TurkeyThis research looked at nonlinear ordinary differential equations with global differential operators and the Dirac-delta and exponential decay kernels. A recently developed numerical approach based on the repetitive use of the well-known midpoint quadrature approximation. Although no theoretical analysis was offered, the method was applied to solve several nonlinear equations in chaos and epidemiology. The observed findings demonstrate the effect of the chosen function gt, for example, a simple SIR model produced chaotic and crossover behaviors.http://www.sciencedirect.com/science/article/pii/S1110016824011682Riemann–Stieltjes integralJacobianGlobal derivative |
| spellingShingle | Abdon Atangana Seda Igret Araz Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators Alexandria Engineering Journal Riemann–Stieltjes integral Jacobian Global derivative |
| title | Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| title_full | Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| title_fullStr | Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| title_full_unstemmed | Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| title_short | Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| title_sort | extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators |
| topic | Riemann–Stieltjes integral Jacobian Global derivative |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011682 |
| work_keys_str_mv | AT abdonatangana extensionofsuccessivemidpointschemefornonlineardifferentialequationswithglobalnonlocaloperators AT sedaigretaraz extensionofsuccessivemidpointschemefornonlineardifferentialequationswithglobalnonlocaloperators |