A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System
In this work, we study the Variational Iteration Method (VIM) accompanied by He's polynomials for obtaining the solution of the temperature distribution in the casting-mould heterogeneous system with fractional order. The combined form of VIM and the Homotopy Perturbation Method (HPM) is called...
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REA Press
2022-06-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_150587_02d9d387f797562ba2ac41bcf83270eb.pdf |
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| author | Muhammad Nadeem |
| author_facet | Muhammad Nadeem |
| author_sort | Muhammad Nadeem |
| collection | DOAJ |
| description | In this work, we study the Variational Iteration Method (VIM) accompanied by He's polynomials for obtaining the solution of the temperature distribution in the casting-mould heterogeneous system with fractional order. The combined form of VIM and the Homotopy Perturbation Method (HPM) is called the Variational Iteration Homotopy Perturbation Method (VIHPM) which yields to implement the system of equations directly. The identification of the Lagrange multiplier is essentially more reliable and higher accurate for such type of problems. The approximate solution converges rapidly to the exact solution which confirms the accuracy of this approach. Some graphical representations are demonstrated to show the validity of this approach. |
| format | Article |
| id | doaj-art-9e15a74e54684210964e2287ffd4cdf7 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-9e15a74e54684210964e2287ffd4cdf72025-01-30T11:20:45ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202022-06-0112526010.22105/cand.2022.150587150587A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous SystemMuhammad Nadeem0Faculty of Science, Yibin University, Yibin 644000, China.In this work, we study the Variational Iteration Method (VIM) accompanied by He's polynomials for obtaining the solution of the temperature distribution in the casting-mould heterogeneous system with fractional order. The combined form of VIM and the Homotopy Perturbation Method (HPM) is called the Variational Iteration Homotopy Perturbation Method (VIHPM) which yields to implement the system of equations directly. The identification of the Lagrange multiplier is essentially more reliable and higher accurate for such type of problems. The approximate solution converges rapidly to the exact solution which confirms the accuracy of this approach. Some graphical representations are demonstrated to show the validity of this approach.https://www.journal-cand.com/article_150587_02d9d387f797562ba2ac41bcf83270eb.pdfvariational iteration methodhomotopy perturbation methodcasting-mould systemapproximate solution |
| spellingShingle | Muhammad Nadeem A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System Computational Algorithms and Numerical Dimensions variational iteration method homotopy perturbation method casting-mould system approximate solution |
| title | A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System |
| title_full | A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System |
| title_fullStr | A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System |
| title_full_unstemmed | A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System |
| title_short | A Semi-Analytical Approach for the Approximate Solution of Casting-Mould Heterogeneous System |
| title_sort | semi analytical approach for the approximate solution of casting mould heterogeneous system |
| topic | variational iteration method homotopy perturbation method casting-mould system approximate solution |
| url | https://www.journal-cand.com/article_150587_02d9d387f797562ba2ac41bcf83270eb.pdf |
| work_keys_str_mv | AT muhammadnadeem asemianalyticalapproachfortheapproximatesolutionofcastingmouldheterogeneoussystem AT muhammadnadeem semianalyticalapproachfortheapproximatesolutionofcastingmouldheterogeneoussystem |