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Higher Order Difference Schemes for the First and Third Boundary Value Problem to \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{r}\;\frac{{\rm d}}{{{\rm d}r}}\left({r\frac{{{\rm d}u}}{{{\rm d}r}}} \right)\; + \;f\left( r\right) \; = \;0 $\end{document}
Author(s) -
Stoyan Gisbert
Publication year - 1975
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19750551103
Subject(s) - order (exchange) , scheme (mathematics) , mathematics , boundary value problem , value (mathematics) , physics , boundary (topology) , mathematical physics , combinatorics , calculus (dental) , mathematical analysis , statistics , medicine , dentistry , finance , economics
Firstly, the exact difference scheme is constructed for the problem posed in [ 0 , R 1 ]. Then, this is used to get a third order difference scheme. For the problem considered in [R 0 , R 1 ], R 0 > 0 , the accuracy of the scheme is also O(h 3 ) (without assumptions on R 0 /h). In the case of 0 < R 0 = O( 1 ) and the first boundary value problem, accuracy increases to be O(h 4 ). The paper contains an ALGOL program implementing the described scheme and some numerical results.