 A discontinuous finite element approximation to singular Lane-Emden type equationsMohammad Izadi Applied Mathematics and Computation, 2021, vol. 401, issue C Abstract: In this article, we develop the local discontinuous Galerkin finite element method for the numerical approximations of a class of singular second-order ordinary differential equations known as the Lane-Emden type equations equipped with initial or boundary conditions. These equations have been considered via different models that naturally appear for example in several phenomena in astrophysical science. By converting the governing equations into a first-order systems of differential equations, the approximate solution is sought in a piecewise discontinuous polynomial space while the natural upwind fluxes are used at element interfaces. The existence-uniqueness of the weak formulation is provided and the numerical stability of the method in the L∞ norm is established. Five illustrative test problems are given to demonstrate the applicability and validity of the scheme. Comparisons between the numerical results of the proposed method with existing results are carried out in order to show that the new approximation algorithm provides accurate solutions even near the singular point. Keywords: Lane-Emden type equations; Local discontinuous Galerkin method; Numerical stability; Singular initial-value problems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001636 DOI: 10.1016/j.amc.2021.126115 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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