Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima”
The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with “maxima.” Th...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/493271 |
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| _version_ | 1841524452227022848 |
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| author | S. Hristova A. Golev |
| author_facet | S. Hristova A. Golev |
| author_sort | S. Hristova |
| collection | DOAJ |
| description | The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with “maxima.” The case when upper and lower solutions of the given problem are known at different initial time is studied. Additionally, all initial value problems for successive approximations have both initial time and initial functions different. It allows us to construct sequences of successive approximations as well as sequences of initial functions, which are convergent to the solution and to the initial function of the given initial value problem, respectively. The suggested algorithm is realized as a computer program, and it is applied to several examples, illustrating the advantages of the suggested scheme. |
| format | Article |
| id | doaj-art-4b2d61ae6b3a453bbb1ed8f8cfa91576 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4b2d61ae6b3a453bbb1ed8f8cfa915762025-02-03T05:53:13ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/493271493271Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima”S. Hristova0A. Golev1Faculty of Mathematics and Informatics, Plovdiv University, Tzar Asen 24, 4000 Plovdiv, BulgariaFaculty of Mathematics and Informatics, Plovdiv University, Tzar Asen 24, 4000 Plovdiv, BulgariaThe object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with “maxima.” The case when upper and lower solutions of the given problem are known at different initial time is studied. Additionally, all initial value problems for successive approximations have both initial time and initial functions different. It allows us to construct sequences of successive approximations as well as sequences of initial functions, which are convergent to the solution and to the initial function of the given initial value problem, respectively. The suggested algorithm is realized as a computer program, and it is applied to several examples, illustrating the advantages of the suggested scheme.http://dx.doi.org/10.1155/2012/493271 |
| spellingShingle | S. Hristova A. Golev Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” Abstract and Applied Analysis |
| title | Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” |
| title_full | Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” |
| title_fullStr | Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” |
| title_full_unstemmed | Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” |
| title_short | Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” |
| title_sort | monotone iterative method for the initial value problem with initial time difference for differential equations with maxima |
| url | http://dx.doi.org/10.1155/2012/493271 |
| work_keys_str_mv | AT shristova monotoneiterativemethodfortheinitialvalueproblemwithinitialtimedifferencefordifferentialequationswithmaxima AT agolev monotoneiterativemethodfortheinitialvalueproblemwithinitialtimedifferencefordifferentialequationswithmaxima |