A cubic spline method for solving the wave equation of nonlinear optics

1974 ◽  
Vol 16 (4) ◽  
pp. 324-341 ◽  
Author(s):  
J.A. Fleck
Keyword(s):  
Wave Equation ◽  
Nonlinear Optics ◽  
Cubic Spline ◽  
Spline Method

scholarly journals Cubic Spline Method for 1D Wave Equation in Polar Coordinates

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
R. K. Mohanty ◽  
Rajive Kumar ◽  
Vijay Dahiya
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Spline Approximation ◽  
Cubic Spline ◽  
Polar Coordinates ◽  
Spline Method ◽  
Implicit Difference Scheme ◽  
Time Direction ◽  
Numerical Examples ◽  
Theoretical Results

Using nonpolynomial cubic spline approximation in space and finite difference in time direction, we discuss three-level implicit difference scheme of O(k2+h4) for the numerical solution of 1D wave equations in polar coordinates, where k>0 and h>0 are grid sizes in time and space coordinates, respectively. The proposed method is applicable to problems with singularity. Stability theory of the proposed method is discussed, and numerical examples are given in support of the theoretical results.

Discrete cubic spline technique for solving one-dimensional Bratu’s problem

2021 ◽  
pp. 2250011
Author(s):  
Pooja Khandelwal ◽  
Arshad Khan ◽  
Talat Sultana
Keyword(s):  
Boundary Value Problems ◽  
Convergence Analysis ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Cubic Spline ◽  
Spline Method ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Bratu’S Problem ◽  
Highly Nonlinear

In this paper, discrete cubic spline method based on central differences is developed to solve one-dimensional (1D) Bratu’s and Bratu’s type highly nonlinear boundary value problems (BVPs). Convergence analysis is briefly discussed. Four examples are given to justify the presented method and comparisons are made to confirm the advantage of the proposed technique.

On the Use of the Inverted Abel Integral for Evaluating Spectroscopic Sources

1981 ◽  
Vol 35 (1) ◽  
pp. 35-42 ◽  
Author(s):  
J. D. Algeo ◽  
M. B. Denton
Keyword(s):  
Noisy Data ◽  
Large Data ◽  
Cubic Spline ◽  
Low Noise ◽  
Large Data Sets ◽  
Small Data ◽  
Data Sets ◽  
Spline Method ◽  
Noise Levels ◽  
Small Data Sets

A numerical method for evaluating the inverted Abel integral employing cubic spline approximations is described along with a modification of the procedure of Cremers and Birkebak, and an extension of the Barr method. The accuracy of the computations is evaluated at several noise levels and with varying resolution of the input data. The cubic spline method is found to be useful only at very low noise levels, but capable of providing good results with small data sets. The Barr method is computationally the simplest, and is adequate when large data sets are available. For noisy data, the method of Cremers and Birkebak gave the best results.

Sign in / Sign up

Export Citation Format

Share Document