Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method
In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. In addition, by finding the solutions of the obtained random complex differential equations, th...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2023/3713454 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547959183507456 |
|---|---|
| author | Mehmet Merdan Merve Merdan Rıdvan Şahin |
| author_facet | Mehmet Merdan Merve Merdan Rıdvan Şahin |
| author_sort | Mehmet Merdan |
| collection | DOAJ |
| description | In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. In addition, by finding the solutions of the obtained random complex differential equations, the probability characteristics of the solutions are examined. The random version of the differential transformation method (DTM) is used to obtain an analytical solution close to the solution of the random differential equation. Approximate expected values and variances are calculated using the approximate solution method. The solutions of some random complex differential equations obtained by using random probability characteristics with gamma, normal, and beta distributions were obtained by the DTM method. The probability characteristics obtained are shown graphically with the help of the MAPLE program. |
| format | Article |
| id | doaj-art-fa0f2da9e301425684671e2dee201d4d |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-fa0f2da9e301425684671e2dee201d4d2025-02-03T06:42:47ZengWileyComplexity1099-05262023-01-01202310.1155/2023/3713454Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation MethodMehmet Merdan0Merve Merdan1Rıdvan Şahin2Department of Mathematical EngineeringDepartment of Mathematical EngineeringDepartment of Mathematical EngineeringIn this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. In addition, by finding the solutions of the obtained random complex differential equations, the probability characteristics of the solutions are examined. The random version of the differential transformation method (DTM) is used to obtain an analytical solution close to the solution of the random differential equation. Approximate expected values and variances are calculated using the approximate solution method. The solutions of some random complex differential equations obtained by using random probability characteristics with gamma, normal, and beta distributions were obtained by the DTM method. The probability characteristics obtained are shown graphically with the help of the MAPLE program.http://dx.doi.org/10.1155/2023/3713454 |
| spellingShingle | Mehmet Merdan Merve Merdan Rıdvan Şahin Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method Complexity |
| title | Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method |
| title_full | Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method |
| title_fullStr | Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method |
| title_full_unstemmed | Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method |
| title_short | Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method |
| title_sort | investigation of behavior on solutions of lane emden complex differential equations by a random differential transformation method |
| url | http://dx.doi.org/10.1155/2023/3713454 |
| work_keys_str_mv | AT mehmetmerdan investigationofbehavioronsolutionsoflaneemdencomplexdifferentialequationsbyarandomdifferentialtransformationmethod AT mervemerdan investigationofbehavioronsolutionsoflaneemdencomplexdifferentialequationsbyarandomdifferentialtransformationmethod AT rıdvansahin investigationofbehavioronsolutionsoflaneemdencomplexdifferentialequationsbyarandomdifferentialtransformationmethod |