scholarly journals Preconditioning Cubic Spline Collocation Methods for a Coupled Elliptic Equation

2010 ◽  
Vol 50 (3) ◽  
pp. 419-431
Author(s):  
Byeong-Chun Shin ◽  
Sang-Dong Kim
Keyword(s):  
Elliptic Equation ◽  
Cubic Spline ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Cubic Spline Collocation

Optimal Superconvergent One Step Nodal Cubic Spline Collocation Methods

2005 ◽  
Vol 27 (2) ◽  
pp. 575-598 ◽  
Author(s):  
Bernard Bialecki ◽  
Graeme Fairweather ◽  
Andreas Karageorghis
Keyword(s):  
Cubic Spline ◽  
Collocation Methods ◽  
Spline Collocation ◽  
One Step ◽  
Cubic Spline Collocation

scholarly journals Pricing American bond options using a cubic spline collocation method

2014 ◽  
Vol 32 (2) ◽  
pp. 189 ◽  
Author(s):  
Abdelmajid El hajaji ◽  
Khalid Hilal ◽  
Abdelhafid Serghini ◽  
El bekkey Mermri
Keyword(s):  
Collocation Method ◽  
Nonlinear Partial Differential Equation ◽  
Method Of Lines ◽  
Cubic Spline ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Penalty Term ◽  
Spline Collocation Method ◽  
Cubic Spline Collocation ◽  
The One

In this paper, American options on a discount bond are priced under the Cox-Ingrosll-Ross (CIR) model. The linear complementarity problem of the option value is solved numerically by a penalty method. The problem is transformed into a nonlinear partial differential equation (PDE) by adding a power penalty term. The solution of the penalized problem converges to the one of the original problem. To numerically solve this nonlinear PDE, we use the horizontal method of lines to discretize the temporal variable and the spatial variable by means of trapezoidal method and a cubic spline collocation method, respectively. We show that this full discretization scheme is second order convergent, and hence the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed. Numerical results are presented and compared with other collocation methods given in the literature.

Modified nodal cubic spline collocation for biharmonic equations

2007 ◽  
Vol 43 (4) ◽  
pp. 331-353 ◽  
Author(s):  
Abeer Ali Abushama ◽  
Bernard Bialecki
Keyword(s):  
Cubic Spline ◽  
Spline Collocation ◽  
Biharmonic Equations ◽  
Cubic Spline Collocation
Sign in / Sign up

Export Citation Format

Share Document