Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System
This study investigates the solution of an ocean waste plastic management system model. The model is represented by a nonlinear system which is divided into three compartments: the waste plastic materials <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=&qu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4601 |
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| author | Mohammad Izadi Mahmood Parsamanesh Waleed Adel |
| author_facet | Mohammad Izadi Mahmood Parsamanesh Waleed Adel |
| author_sort | Mohammad Izadi |
| collection | DOAJ |
| description | This study investigates the solution of an ocean waste plastic management system model. The model is represented by a nonlinear system which is divided into three compartments: the waste plastic materials <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">W</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, marine debris <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">M</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and the process of recycling <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>. These compartments form a simulated model that is solved using two collocation techniques based on a shifted version of the Morgan-Voyce (MV) functions, while the first matrix collocation procedure is directly applied to the given model, in the second approach we fuse the technique of quasilinearization together with the shifted MV (SMV) collocation strategy. Moreover, we give the basic reproduction number and discuss the existence of equilibria and the local stability of equilibria are investigated. The basic definitions of the SMV polynomials are introduced and detailed convergence analysis of the related power series expansion in both weighted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>2</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mo>∞</mo></msub></semantics></math></inline-formula> norms are presented. Diverse numerical simulations are performed to prove the accurateness and effectiveness of the presented approaches and the results ate illustrated through tables and figures. |
| first_indexed | 2024-03-09T17:40:37Z |
| format | Article |
| id | doaj.art-52ba04f230db40738243f061a8a8c9a8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:37Z |
| publishDate | 2022-12-01 |
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| series | Mathematics |
| spelling | doaj.art-52ba04f230db40738243f061a8a8c9a82023-11-24T11:36:17ZengMDPI AGMathematics2227-73902022-12-011023460110.3390/math10234601Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean SystemMohammad Izadi0Mahmood Parsamanesh1Waleed Adel2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, IranDepartment of Mathematics, Technical and Vocational University (TVU), Tehran 14357-61137, IranDepartment of Technology of Informatics and Communications, Université Francaise d’Egypte, Ismailia Desert Road, El Shorouk, Cairo 11837, EgyptThis study investigates the solution of an ocean waste plastic management system model. The model is represented by a nonlinear system which is divided into three compartments: the waste plastic materials <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">W</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, marine debris <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">M</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and the process of recycling <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>. These compartments form a simulated model that is solved using two collocation techniques based on a shifted version of the Morgan-Voyce (MV) functions, while the first matrix collocation procedure is directly applied to the given model, in the second approach we fuse the technique of quasilinearization together with the shifted MV (SMV) collocation strategy. Moreover, we give the basic reproduction number and discuss the existence of equilibria and the local stability of equilibria are investigated. The basic definitions of the SMV polynomials are introduced and detailed convergence analysis of the related power series expansion in both weighted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>2</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mo>∞</mo></msub></semantics></math></inline-formula> norms are presented. Diverse numerical simulations are performed to prove the accurateness and effectiveness of the presented approaches and the results ate illustrated through tables and figures.https://www.mdpi.com/2227-7390/10/23/4601collocation pointsconvergent analysisshifted Morgan-Voyce functionsocean systemwaste plastic management |
| spellingShingle | Mohammad Izadi Mahmood Parsamanesh Waleed Adel Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System Mathematics collocation points convergent analysis shifted Morgan-Voyce functions ocean system waste plastic management |
| title | Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System |
| title_full | Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System |
| title_fullStr | Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System |
| title_full_unstemmed | Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System |
| title_short | Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System |
| title_sort | numerical and stability investigations of the waste plastic management model in the ocean system |
| topic | collocation points convergent analysis shifted Morgan-Voyce functions ocean system waste plastic management |
| url | https://www.mdpi.com/2227-7390/10/23/4601 |
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