Numerical analysis of the eigenfunctions for the combustion of a non-linear medium in the radial-symmetric case

A method is developed for the numerical solution of a selfsimilar boundary-value problem which arises in the investigation of the unbounded solutions of the Cauchy problem for the non-linear heat conduction equation with a source. It is based on the use of a continuous analogue of Newton's meth...

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Bibliographic Details
Published in:U.S.S.R. computational mathematics and mathematical physics 1989, Vol.29 (6), p.61-73
Main Authors: Dimova, S.N., Kaschiyev, M.S., Kurdyumov, S.P.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Numerical approximation and analysis
Physics
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Summary:A method is developed for the numerical solution of a selfsimilar boundary-value problem which arises in the investigation of the unbounded solutions of the Cauchy problem for the non-linear heat conduction equation with a source. It is based on the use of a continuous analogue of Newton's method and the finite element method. The convergence and accuracy of the proposed method are investigated numerically as are the structure and behaviour of the solution of the selfsimilar problem in certain interesting limiting cases. In the cylindrically and spherically symmetric cases, solutions with a new structure are obtained which vanish in the neighbourhood of the centre of symmetry.
ISSN:0041-5553
DOI:10.1016/S0041-5553(89)80008-4