Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations
In this article, a simple and new algorithm is proposed, namely the modified variational iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order Korteweg de-Vries (KdV) equations. In order to verify the precision, accuracy and stability of the mVIA-I metho...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Chamran University of Ahvaz
2020-12-01
|
| Series: | Journal of Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | https://jacm.scu.ac.ir/article_15511_e3bf616a2a4b0efa4193b56946a41e27.pdf |
| _version_ | 1818444856719048704 |
|---|---|
| author | Hijaz Ahmad Tufail A. Khan Predrag S. Stanimirovic Imtiaz Ahmad |
| author_facet | Hijaz Ahmad Tufail A. Khan Predrag S. Stanimirovic Imtiaz Ahmad |
| author_sort | Hijaz Ahmad |
| collection | DOAJ |
| description | In this article, a simple and new algorithm is proposed, namely the modified variational iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order Korteweg de-Vries (KdV) equations. In order to verify the precision, accuracy and stability of the mVIA-I method, generated numerical results are compared with the Laplace decomposition method, Adomian decomposition method, Homotopy perturbation transform method and the modified Adomian decomposition method. Comparison with the mentioned methods reveals that the mVIA-I is computationally attractive, exceptionally productive and achieves better accuracy than the others. |
| first_indexed | 2024-12-14T19:22:35Z |
| format | Article |
| id | doaj.art-ef24bda2fe2f4c3391f08c4767ee234f |
| institution | Directory Open Access Journal |
| issn | 2383-4536 2383-4536 |
| language | English |
| last_indexed | 2024-12-14T19:22:35Z |
| publishDate | 2020-12-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-ef24bda2fe2f4c3391f08c4767ee234f2022-12-21T22:50:18ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362020-12-016Special Issue1220122710.22055/jacm.2020.33305.219715511Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type EquationsHijaz Ahmad0Tufail A. Khan1Predrag S. Stanimirovic2Imtiaz Ahmad3Department of Basic Sciences, University of Engineering and Technology Peshawar, PakistanDepartment of Basic Sciences, University of Engineering and Technology Peshawar, PakistanFaculty of Science and Mathematics, University of Niš, Višegradska 33, Nis 18000, SerbiaDepartment of Mathematics, University of Swabi, Swabi, Khyber Pakhtunkhwa, PakistanIn this article, a simple and new algorithm is proposed, namely the modified variational iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order Korteweg de-Vries (KdV) equations. In order to verify the precision, accuracy and stability of the mVIA-I method, generated numerical results are compared with the Laplace decomposition method, Adomian decomposition method, Homotopy perturbation transform method and the modified Adomian decomposition method. Comparison with the mentioned methods reveals that the mVIA-I is computationally attractive, exceptionally productive and achieves better accuracy than the others.https://jacm.scu.ac.ir/article_15511_e3bf616a2a4b0efa4193b56946a41e27.pdfkorteweg–de vries equationmodification of variational iteration algorithm-ififth order kdv equationgeneralized kdv equation |
| spellingShingle | Hijaz Ahmad Tufail A. Khan Predrag S. Stanimirovic Imtiaz Ahmad Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations Journal of Applied and Computational Mechanics korteweg–de vries equation modification of variational iteration algorithm-i fifth order kdv equation generalized kdv equation |
| title | Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations |
| title_full | Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations |
| title_fullStr | Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations |
| title_full_unstemmed | Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations |
| title_short | Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations |
| title_sort | modified variational iteration technique for the numerical solution of fifth order kdv type equations |
| topic | korteweg–de vries equation modification of variational iteration algorithm-i fifth order kdv equation generalized kdv equation |
| url | https://jacm.scu.ac.ir/article_15511_e3bf616a2a4b0efa4193b56946a41e27.pdf |
| work_keys_str_mv | AT hijazahmad modifiedvariationaliterationtechniqueforthenumericalsolutionoffifthorderkdvtypeequations AT tufailakhan modifiedvariationaliterationtechniqueforthenumericalsolutionoffifthorderkdvtypeequations AT predragsstanimirovic modifiedvariationaliterationtechniqueforthenumericalsolutionoffifthorderkdvtypeequations AT imtiazahmad modifiedvariationaliterationtechniqueforthenumericalsolutionoffifthorderkdvtypeequations |