A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method. (English) Zbl 1336.65178
Summary: The present paper uses a relatively new approach and methodology to solve second order two dimensional hyperbolic telegraph equation numerically. We use modified cubic B-spline basis functions based differential quadrature method for space discretization that reduces the problem into an amenable system of ordinary differential equations. The resulting system of ODEs in time subsequently have been solved by SSP-RK43 scheme. Stability of the scheme is studied using matrix stability analysis and found to be stable. The efficacy of proposed approach has been confirmed with seven numerical experiments, where comparison is made with some earlier work. It is clear that the results obtained are acceptable and are in good agreement with earlier studies. However, we obtain these results in much less CPU time. The method is very simple, efficient and produces very accurate numerical results in considerably smaller number of nodes and hence saves computational effort.
MSC:
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
Keywords:
differential quadrature method; hyperbolic telegraph equation; modified B-spline basis functions; Thomas algorithmReferences:
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