scholarly journals ALGORITHMIC SOFTWARE FOR USING THE CUBIC SPLINE IN RESTORING THE FUNCTIONAL DEPENDENCE IN THE CASE OF BOUNDARY CONDITIONS FOR THE FIRST DERIVATIVES

2021 ◽  
Vol 21 ◽  
pp. 114-121
Author(s):  
E Eremeev ◽  
◽  
A Rackovich ◽  
Keyword(s):  
Boundary Conditions ◽  
Functional Dependence ◽  
Cubic Spline ◽  
Algorithmic Software

HIGHER-ORDER PARAMETER UNIFORM CONVERGENT SCHEMES FOR ROBIN TYPE REACTION-DIFFUSION PROBLEMS USING ADAPTIVELY GENERATED GRID

2012 ◽  
Vol 09 (04) ◽  
pp. 1250052 ◽  
Author(s):  
PRATIBHAMOY DAS ◽  
SRINIVASAN NATESAN
Keyword(s):  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Perturbation Parameter ◽  
Cubic Spline ◽  
Diffusion Problem ◽  
Central Difference ◽  
Monitor Function ◽  
Type Boundary ◽  
Robin Boundary ◽  
Interior Points

In this article, a singularly perturbed reaction-diffusion problem with Robin boundary conditions, is considered. In general, the solution of this problem possesses boundary layers at both the ends of the domain. To solve this problem, we propose a numerical scheme, involving the cubic spline scheme for boundary conditions and the classical central difference scheme for the differential equation (DE) at the interior points. The grid is generated by the equidistribution of a positive monitor function. It has been proved that classical forward–backward approximation for mixed type boundary conditions, gives first-order convergence, whereas our proposed cubic spline scheme provides second-order accuracy independent of the perturbation parameter. Numerical experiments have been provided to validate the theoretical results.

scholarly journals Fitting Rainfall Data by Using Cubic Spline Interpolation

2018 ◽  
Vol 225 ◽  
pp. 05001
Author(s):  
Irham Azizan ◽  
Samsul Ariffin Bin Abdul Karim ◽  
S. Suresh Kumar Raju
Keyword(s):  
Missing Data ◽  
Boundary Conditions ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Rainfall Data ◽  
Data Imputation ◽  
Monthly Basis ◽  
Missing Data Imputation ◽  
Cubic Spline Interpolation ◽  
Hermite Interpolating Polynomial

This study discusses the application of two cubic spline i.e. natural and not-a-knot end boundary conditions to visualize and predict the rainfall data. The interpolation and the analysis of the rainfall data will be done on a monthly basis by using the MATLAB software. The rainfall data is obtained from Malaysia Meteorology Department for Ipoh and Petaling Jaya in year 2014 and 2015. The interpolating curves are then being compared and if there is any negative value on the interpolating curve on some sub-interval, that part will be replaced by using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). We discuss the missing data imputation by using both splines.

Cubic Spline Wavelets Satisfying Homogeneous Boundary Conditions for Fourth-Order Problems

2009 ◽  
Author(s):  
Dana Černá ◽  
Václav Finěk ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Cubic Spline ◽  
Spline Wavelets ◽  
Fourth Order Problems

On the Dimension of Bivariate C1 Cubic Spline Space with Homogeneous Boundary Conditions over a CT Triangulation

2011 ◽  
Vol 50-51 ◽  
pp. 488-492
Author(s):  
Dian Xuan Gong ◽  
Feng Gong Lang
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Numerical Approximation ◽  
Cubic Spline ◽  
Spline Space ◽  
Singular Boundary ◽  
Piecewise Polynomial ◽  
Nite Element ◽  
Bivariate Spline ◽  
Aided Design

A bivariate spline is a piecewise polynomial with some smoothness de ned on a parti- tion. In this paper, we mainly study the dimensions of bivariate C1 cubic spline spaces S1;0 3 (CT ) and S1;1 3 (CT ) with homogeneous boundary conditions over CT by using interpolating technique, where CT stands for a CT triangulation. The dimensions are related with the numbers of the inter vertices and the singular boundary vertices. The results of this paper can be applied in many elds such as the nite element method for partial di erential equation, computer aided design, numerical approximation, and so on.

Cubic spline wavelets with four vanishing moments on the interval and their applications to option pricing under Kou model

2019 ◽  
Vol 17 (01) ◽  
pp. 1850061 ◽  
Author(s):  
Dana Černá
Keyword(s):  
Boundary Conditions ◽  
Option Pricing ◽  
Cubic Spline ◽  
Dirichlet Boundary Conditions ◽  
Vanishing Moments ◽  
Spline Wavelet ◽  
Spline Wavelets ◽  
Jump Diffusion Model ◽  
The Stability ◽  
Homogeneous Dirichlet Boundary Conditions

The paper is concerned with the construction of a cubic spline wavelet basis on the unit interval and an adaptation of this basis to the first-order homogeneous Dirichlet boundary conditions. The wavelets have four vanishing moments and they have the shortest possible support among all cubic spline wavelets with four vanishing moments corresponding to B-spline scaling functions. We provide a rigorous proof of the stability of the basis in the space [Formula: see text] or its subspace incorporating boundary conditions. To illustrate the applicability of the constructed bases, we apply the wavelet-Galerkin method to option pricing under the double exponential jump-diffusion model and we compare the results with other cubic spline wavelet bases and with other methods.

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