Numerical Algorithms

, Volume 74, Issue 2, pp 289–306 | Cite as

Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term

Original Paper
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Abstract

In this paper, two classes of methods are developed for the solution of two space dimensional wave equations with a nonlinear source term. We have used non-polynomial cubic spline function approximations in both space directions. The methods involve some parameters, by suitable choices of the parameters, a new high accuracy three time level scheme of order O(h 4 + k 4 + τ 2 + τ 2 h 2 + τ 2 k 2) has been obtained. Stability analysis of the methods have been carried out. The results of some test problems are included to demonstrate the practical usefulness of the proposed methods. The numerical results for the solution of two dimensional sine-Gordon equation are compared with those already available in literature.

Keywords

Non-polynomial spline approximation Two-dimensional wave equation Stability analysis Sine-Gordon equation 

Mathematics Subject Classification (2010)

65D07 65M12 65M22 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Central Tehran BranchIslamic Azad UniversityTehranIran

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