Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere

2002 ◽  
Vol 179 (2) ◽  
pp. 578-592 ◽  
Author(s):  
Anita T. Layton
Keyword(s):  
Shallow Water ◽  
Collocation Method ◽  
Shallow Water Equations ◽  
Cubic Spline ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Cubic Spline Collocation

scholarly journals Cubic Spline Collocation Method for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Shui-Ping Yang ◽  
Ai-Guo Xiao
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Cubic Spline ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Fractional Differential ◽  
Cubic Spline Collocation ◽  
The Stability ◽  
Two Parameters

We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence, and the stability of this method for IVPs of FDEs are obtained. Some numerical examples verify our theoretical results.

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.

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