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Spline methods for the solution of hyperbolic equation with variable coefficients
Authors:J Rashidinia  R Mohammadi  R Jalilian
Institution:1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran;2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
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(k2 + h2) and O(k2 + h4). 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
Keywords:second‐order hyperbolic equation  non‐polynomial cubic spline  stability analysis
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