New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates-Reference-Cited by-同舟云学术

New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates

Published:2013-09-30 Issue: Volume:2013 Page:1-8
ISSN:1687-9562
Container-title:Advances in Numerical Analysis
language:en
Short-container-title:Advances in Numerical Analysis

Author:

Gopal Venu¹^ORCID,Mohanty R. K.²,Jha Navnit²

Affiliation:

1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India

2. Department of Applied Mathematics, South Asian University, Akbar Bhawan, Delhi 110021, India

Abstract

We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

Publisher

Hindawi Limited

Link

http://downloads.hindawi.com/archive/2013/470480.pdf

Reference23 articles.

1. Piecewise Cubic Interpolation and Two-Point Boundary Problems

2. The use of cubic splines in the solution of two-point boundary value problems

3. A Cubic Spline Technique for the One Dimensional Heat Conduction Equation

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

5. A Fully Implicit Finite Difference Approximation to the One-dimensional Wave Equation using a Cubic Spline Techinique

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