Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method
In this paper, an efficient perturbation algorithm combining the method of Multiple Scales and Modified Lindstedt–Poincare Techniques is proposed to solve the equation of Van der Pol oscillator with very strong nonlinearity. This algorithm combines the advantages of both methods. Solution of Van der...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences, India, Section A, physical sciences India, Section A, physical sciences, 2021-03, Vol.91 (1), p.55-65 |
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| container_title | Proceedings of the National Academy of Sciences, India, Section A, physical sciences |
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| creator | Kumar, Manoj Varshney, Parul |
| description | In this paper, an efficient perturbation algorithm combining the method of Multiple Scales and Modified Lindstedt–Poincare Techniques is proposed to solve the equation of Van der Pol oscillator with very strong nonlinearity. This algorithm combines the advantages of both methods. Solution of Van der Pol equation by the Multiple Scales Modified Lindstedt–Poincare (MSMLP) method is compared with the Multiple Scales method and numerical solution using MATLAB 7.8. The convergence criterion for the solution by Multiple Scales and MSMLP methods is discussed and shown that Multiple Scales method fails the convergence criterion for large values of small parameter, while MSMLP method satisfies the convergence criterion for both small and large values. Numerical simulation has been performed in MATLAB 7.8 for different values of small parameter to prove the efficiency and accuracy of the proposed method. |
| doi_str_mv | 10.1007/s40010-019-00655-y |
| format | Article |
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This algorithm combines the advantages of both methods. Solution of Van der Pol equation by the Multiple Scales Modified Lindstedt–Poincare (MSMLP) method is compared with the Multiple Scales method and numerical solution using MATLAB 7.8. The convergence criterion for the solution by Multiple Scales and MSMLP methods is discussed and shown that Multiple Scales method fails the convergence criterion for large values of small parameter, while MSMLP method satisfies the convergence criterion for both small and large values. Numerical simulation has been performed in MATLAB 7.8 for different values of small parameter to prove the efficiency and accuracy of the proposed method.</description><identifier>ISSN: 0369-8203</identifier><identifier>EISSN: 2250-1762</identifier><identifier>DOI: 10.1007/s40010-019-00655-y</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Algorithms ; Applied and Technical Physics ; Atomic ; Computer simulation ; Convergence ; Criteria ; Matlab ; Molecular ; Multiscale analysis ; Optical and Plasma Physics ; Parameters ; Perturbation ; Physics ; Physics and Astronomy ; Quantum Physics ; Research Article</subject><ispartof>Proceedings of the National Academy of Sciences, India, Section A, physical sciences, 2021-03, Vol.91 (1), p.55-65</ispartof><rights>The National Academy of Sciences, India 2020</rights><rights>The National Academy of Sciences, India 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-d4c1ccfebcbbd3a4fac71934019bb874ee20997a89b65c7313d35ecacf95ea633</citedby><cites>FETCH-LOGICAL-c319t-d4c1ccfebcbbd3a4fac71934019bb874ee20997a89b65c7313d35ecacf95ea633</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40010-019-00655-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40010-019-00655-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Kumar, Manoj</creatorcontrib><creatorcontrib>Varshney, Parul</creatorcontrib><title>Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method</title><title>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</title><addtitle>Proc. 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Numerical simulation has been performed in MATLAB 7.8 for different values of small parameter to prove the efficiency and accuracy of the proposed method.</description><subject>Algorithms</subject><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Computer simulation</subject><subject>Convergence</subject><subject>Criteria</subject><subject>Matlab</subject><subject>Molecular</subject><subject>Multiscale analysis</subject><subject>Optical and Plasma Physics</subject><subject>Parameters</subject><subject>Perturbation</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Research Article</subject><issn>0369-8203</issn><issn>2250-1762</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWLQv4CrgejQ_M5lmKaX-QKuFWrchk9ypKdNJTWYW3fkOvqFPYnQEd97Nhcv5zuEehC4ouaKElNcxJ4SSjFCZESKKIjscoRFjBcloKdgxGhEuZDZhhJ-icYxbkqYoJRP5CG0e-x0EZ3SDV27XN7pzvsW-xi-6xRYCXvoGz9764b6Ort3gRd90bt8AXiUMIl5462oHFs9da2MHtvt8_1h61xodAC-ge_X2HJ3Uuokw_t1naH07e57eZ_Onu4fpzTwznMous7mhxtRQmaqyXOe1NiWVPE-_VdWkzAEYkbLUE1mJwpSccssLMNrUsgAtOD9Dl4PvPvi3HmKntr4PbYpULJdclrkUIqnYoDLBxxigVvvgdjocFCXqu1M1dKpSrvrpVB0SxAcoJnG7gfBn_Q_1BT3afG0</recordid><startdate>20210301</startdate><enddate>20210301</enddate><creator>Kumar, Manoj</creator><creator>Varshney, Parul</creator><general>Springer India</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210301</creationdate><title>Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method</title><author>Kumar, Manoj ; Varshney, Parul</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-d4c1ccfebcbbd3a4fac71934019bb874ee20997a89b65c7313d35ecacf95ea633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Computer simulation</topic><topic>Convergence</topic><topic>Criteria</topic><topic>Matlab</topic><topic>Molecular</topic><topic>Multiscale analysis</topic><topic>Optical and Plasma Physics</topic><topic>Parameters</topic><topic>Perturbation</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Research Article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kumar, Manoj</creatorcontrib><creatorcontrib>Varshney, Parul</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kumar, Manoj</au><au>Varshney, Parul</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method</atitle><jtitle>Proceedings of the National Academy of Sciences, India, Section A, physical sciences</jtitle><stitle>Proc. 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| subjects | Algorithms Applied and Technical Physics Atomic Computer simulation Convergence Criteria Matlab Molecular Multiscale analysis Optical and Plasma Physics Parameters Perturbation Physics Physics and Astronomy Quantum Physics Research Article |
| title | Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method |
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