Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equations
We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the inter...
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Published in | Numerical algorithms Vol. 64; no. 2; pp. 349 - 383 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Boston
Springer US
01.10.2013
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
ISSN | 1017-1398 1572-9265 |
DOI | 10.1007/s11075-012-9669-4 |
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Summary: | We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform
partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson’s equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost
. For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
ISSN: | 1017-1398 1572-9265 |
DOI: | 10.1007/s11075-012-9669-4 |