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Spline methods for the solution of hyperbolic equation with variable coefficients
Author(s) -
Rashidinia J.,
Mohammadi R.,
Jalilian R.
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20229
Subject(s) - mathematics , spline (mechanical) , thin plate spline , partial differential equation , singularity , hyperbolic partial differential equation , mathematical analysis , partial derivative , smoothing spline , variable (mathematics) , m spline , hermite spline , perfect spline , spline interpolation , statistics , structural engineering , engineering , bilinear interpolation
Abstract In this study, we developed the methods based on nonpolynomial cubic spline for numerical solution of second‐order nonhomogeneous hyperbolic partial differential equation. Using nonpolynomial cubic spline in space and finite difference in time directions, we obtained the implicit three level methods of O ( k 2 + h 2 ) and O ( k 2 + h 4 ). The proposed methods are applicable to the problems having singularity at x = 0, too. Stability analysis of the presented methods have been carried out. The presented methods are applied to the nonhomogeneous examples of different types. Numerical comparison with Mohanty's method (Mohanty, Appl Math Comput, 165 (2005), 229–236) shows the superiority of our presented schemes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007