Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique
This paper presents a comparative study of analytical and numerical approaches for solving generalized forms of second-order Hill’s and Meissner’s ordinary differential equations (ODEs), which model a wide range of periodic and oscillatory phenomena in applied mathematics and physics. Using the Akba...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/7237496 |
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| author | Asifa Tassaddiq Sania Qureshi Javed Rehman Larik Amanullah Soomro Fozia Shaikh Evren Hincal Kwara Nantomah |
| author_facet | Asifa Tassaddiq Sania Qureshi Javed Rehman Larik Amanullah Soomro Fozia Shaikh Evren Hincal Kwara Nantomah |
| author_sort | Asifa Tassaddiq |
| collection | DOAJ |
| description | This paper presents a comparative study of analytical and numerical approaches for solving generalized forms of second-order Hill’s and Meissner’s ordinary differential equations (ODEs), which model a wide range of periodic and oscillatory phenomena in applied mathematics and physics. Using the Akbari–Ganji Method (AGM), a powerful semianalytical technique, we derive approximate solutions that effectively capture the essential behavior of these equations. To assess the accuracy and reliability of AGM, we compare its solutions with those obtained using the Fehlberg fourth-fifth order Runge–Kutta method with degree four interpolant (RKF45), a robust numerical method. The comparison involves a detailed error analysis, including the computation of absolute error, maximum absolute error, norm error, root mean square error (RMSE), and Average Error. Results demonstrate that AGM offers high precision and computational efficiency while maintaining agreement with RKF45 numerical solutions. This work highlights AGM’s effectiveness in handling periodic coefficients and broadens its scope within periodic and quasi-periodic systems, providing a promising alternative for researchers tackling complex oscillatory systems. |
| format | Article |
| id | doaj-art-d7b9dba576ab4a1c961ac2e4e7ffd7fc |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d7b9dba576ab4a1c961ac2e4e7ffd7fc2025-08-20T03:31:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/7237496Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical TechniqueAsifa Tassaddiq0Sania Qureshi1Javed Rehman Larik2Amanullah Soomro3Fozia Shaikh4Evren Hincal5Kwara Nantomah6Department of Computer ScienceDepartment of Basic Sciences and Related StudiesDepartment of Mechanical EngineeringDepartment of Basic Sciences and Related StudiesDepartment of Basic Sciences and Related StudiesDepartment of MathematicsDepartment of MathematicsThis paper presents a comparative study of analytical and numerical approaches for solving generalized forms of second-order Hill’s and Meissner’s ordinary differential equations (ODEs), which model a wide range of periodic and oscillatory phenomena in applied mathematics and physics. Using the Akbari–Ganji Method (AGM), a powerful semianalytical technique, we derive approximate solutions that effectively capture the essential behavior of these equations. To assess the accuracy and reliability of AGM, we compare its solutions with those obtained using the Fehlberg fourth-fifth order Runge–Kutta method with degree four interpolant (RKF45), a robust numerical method. The comparison involves a detailed error analysis, including the computation of absolute error, maximum absolute error, norm error, root mean square error (RMSE), and Average Error. Results demonstrate that AGM offers high precision and computational efficiency while maintaining agreement with RKF45 numerical solutions. This work highlights AGM’s effectiveness in handling periodic coefficients and broadens its scope within periodic and quasi-periodic systems, providing a promising alternative for researchers tackling complex oscillatory systems.http://dx.doi.org/10.1155/ijmm/7237496 |
| spellingShingle | Asifa Tassaddiq Sania Qureshi Javed Rehman Larik Amanullah Soomro Fozia Shaikh Evren Hincal Kwara Nantomah Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique International Journal of Mathematics and Mathematical Sciences |
| title | Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique |
| title_full | Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique |
| title_fullStr | Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique |
| title_full_unstemmed | Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique |
| title_short | Solving Generalized Hill’s and Meissner’s Equations by a Semianalytical Technique |
| title_sort | solving generalized hill s and meissner s equations by a semianalytical technique |
| url | http://dx.doi.org/10.1155/ijmm/7237496 |
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