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Solving differential equations with Fourier series and Evolution Strategies

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dc.contributor.authorChaquet, José M.
dc.contributor.authorCarmona, Enrique J.
dc.date.accessioned2024-08-21T12:13:32Z
dc.date.available2024-08-21T12:13:32Z
dc.date.issued2012-09
dc.description.abstractA novel mesh-free approach for solving differential equations based on Evolution Strategies (ESs) is presented. Any structure is assumed in the equations making the process general and suitable for linear and nonlinear ordinary and partial differential equations (ODEs and PDEs), as well as systems of ordinary differential equations (SODEs). Candidate solutions are expressed as partial sums of Fourier series. Taking advantage of the decreasing absolute value of the harmonic coefficients with the harmonic order, several ES steps are performed. Harmonic coefficients are taken into account one by one starting with the lower order ones. Experimental results are reported on several problems extracted from the literature to illustrate the potential of the proposed approach. Two cases (an initial value problem and a boundary condition problem) have been solved using numerical methods and a quantitative comparative is performed. In terms of accuracy and storing requirements the proposed approach outperforms the numerical algorithm.en
dc.description.versionversión final
dc.identifier.doihttp://dx.doi.org/10.1016/j.asoc.2012.05.014
dc.identifier.issn1872-9681
dc.identifier.urihttps://hdl.handle.net/20.500.14468/23283
dc.journal.issue9
dc.journal.titleApplied Soft Computing
dc.journal.volume12
dc.language.isoen
dc.publisherElsevier
dc.relation.centerFacultades y escuelas::E.T.S. de Ingeniería Informática
dc.relation.departmentInteligencia Artificial
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subject.keywordsDifferential equations
dc.subject.keywordsFourier series
dc.subject.keywordsevolution strategies
dc.subject.keywordsmesh-free methods
dc.subject.keywordsharmonic analysis
dc.titleSolving differential equations with Fourier series and Evolution Strategieses
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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