On the deviation of a parametric cubic spline interpolant from its data polygon

2008 ◽  
Vol 25 (3) ◽  
pp. 148-156 ◽  
Author(s):  
Michael S. Floater
Keyword(s):  
Cubic Spline ◽  
Spline Interpolant ◽  
Parametric Cubic Spline

Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline

2018 ◽  
Vol 19 (3-4) ◽  
pp. 357-365 ◽  
Author(s):  
A. S. V. Ravi Kanth ◽  
P. Murali Mohan Kumar
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Cubic Spline ◽  
Singularly Perturbed ◽  
Delay Term ◽  
Second Order Convergence ◽  
Delay Differential ◽  
Parametric Cubic Spline

AbstractIn this paper, we study the numerical method for a class of nonlinear singularly perturbed delay differential equations using parametric cubic spline. Quasilinearization process is applied to convert the nonlinear singularly perturbed delay differential equations into a sequence of linear singularly perturbed delay differential equations. When the delay is not sufficiently smaller order of the singular perturbation parameter, the approach of expanding the delay term in Taylor’s series may lead to bad approximation. To handle the delay term, we construct a special type of mesh in such a way that the term containing delay lies on nodal points after discretization. The parametric cubic spline is presented for solving sequence of linear singularly perturbed delay differential equations. The error analysis of the method is presented and shows second-order convergence. The effect of delay parameter on the boundary layer behavior of the solution is discussed with two test examples.

Novel Approaches to the Parametric Cubic-Spline Interpolation

2013 ◽  
Vol 22 (3) ◽  
pp. 1233-1241 ◽  
Author(s):  
Shao-Hua Hong ◽  
Lin Wang ◽  
Trieu-Kien Truong ◽  
Tsung-Ching Lin ◽  
Lung-Jen Wang
Keyword(s):  
Spline Interpolation ◽  
Cubic Spline ◽  
Cubic Spline Interpolation ◽  
Novel Approaches ◽  
Parametric Cubic Spline
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