Modified Nodal Cubic Spline Collocation For Poisson's Equation

2008 ◽  
Vol 46 (1) ◽  
pp. 397-418 ◽  
Author(s):  
Abeer Ali Abushama ◽  
Bernard Bialecki
Keyword(s):  
Cubic Spline ◽  
Poisson’S Equation ◽  
Spline Collocation ◽  
Poisson's Equation ◽  
Cubic Spline Collocation

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

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 Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
R. K. Mohanty ◽  
Rajive Kumar ◽  
Vijay Dahiya
Keyword(s):  
Iterative Method ◽  
Spline Approximation ◽  
Cubic Spline ◽  
Poisson’S Equation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Poisson's Equation ◽  
Polar Coordinate ◽  
Cylindrical Polar Coordinates ◽  
Diffusion Convection

Using nonpolynomial cubic spline approximation in x- and finite difference in y-direction, we discuss a numerical approximation of O(k2+h4) for the solutions of diffusion-convection equation, where k>0 and h>0 are grid sizes in y- and x-coordinates, respectively. We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates. Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.

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.

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