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...

Full description

Saved in:
Bibliographic Details
Published inNumerical algorithms Vol. 64; no. 2; pp. 349 - 383
Main Authors Bialecki, Bernard, Karageorghis, Andreas
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.10.2013
Springer Nature B.V
Subjects
Online AccessGet full text
ISSN1017-1398
1572-9265
DOI10.1007/s11075-012-9669-4

Cover

More Information
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.
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