Quadratic spline collocation for one-dimensional linear parabolic partial differential equations

Christara, Christina C., Chen, Tong and Dang, Duy-Minh (2010) Quadratic spline collocation for one-dimensional linear parabolic partial differential equations. Numerical Algorithms, 53 4: 511-553. doi:10.1007/s11075-009-9317-9


Author Christara, Christina C.
Chen, Tong
Dang, Duy-Minh
Title Quadratic spline collocation for one-dimensional linear parabolic partial differential equations
Journal name Numerical Algorithms   Check publisher's open access policy
ISSN 1017-1398
1572-9265
Publication date 2010-04-01
Year available 2009
Sub-type Article (original research)
DOI 10.1007/s11075-009-9317-9
Volume 53
Issue 4
Start page 511
End page 553
Total pages 43
Place of publication New York, NY, United States
Publisher Springer New York
Language eng
Formatted abstract
New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The main computational requirements of the most efficient method are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth order. The stability and convergence properties of some of the new methods are analyzed for a model problem. Numerical results demonstrate the stability and accuracy of the methods. Adaptive mesh techniques are introduced in the space dimension, and the resulting method is applied to the American put option pricing problem, giving very competitive results.
Keyword Quadratic splines
Collocation
Parabolic PDEs
Crank-Nicolson
Stability
Optimal order of convergence
American options
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Published online: 17 July 2009

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 09 Oct 2014, 19:06:40 EST by Jon Swabey on behalf of School of Mathematics & Physics