# The Use Of Chebyshev Cardinal Functions For Solution Of The Second‐order One‐dimensional Telegraph Equation

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### Chebyshev Spectral Collocation Method for Computing Nu

tion. A numerical scheme is developed in [11] to solve the one-dimensional hyperbolic telegraph equation using collocation points [11] and approximating the solution using a thin plate splines radial basis function. Another numerical method is presented in [12] to solve the one-dimensional hyperbolic telegraph equation using Chebyshev cardinal

### Research Article A Collocation Method for Numerical Solution

Dehghan and Lakestani [ ] used the Chebyshev cardinal functions, whereas Saadatmandi and Dehghan [ ]used the Chebyshev tau method for expanding the approximate solution of one-dimensional telegraph equation. Mohebbi and Dehghan [ ] reported a higher order compact ni te di erence approximation of fourth order in space and used

### A Solution to the Telegraph Equation by Using DGJ Method

second-order linear hyperbolic equation, Dehgan and Lakestani [10] used a numerical technique consisting of expand-ing the approximate solution as the elements of Chebyshev cardinal functions. Biazar et al. [11] applied the variational iteration method to obtain an approximate solution of the telegraph equation. Saadatmandi and Dehghan [12

### ARTICLE IN PRESS

Second-order hyperbolic telegraph equation Radial basis functions (RBFs) abstract In this paper, we use a numerical method based on the boundary integral equation (BIE) and an application of the dual reciprocity method (DRM) to solve the second-order one space-dimensional hyperbolic telegraph equation.

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Dehghan, M., Lakestani, M., The use of Chebyshev cardinal functions for solution of the second-order one-dimensional telegraph equation Numerical Methods for Partial Differential Equations 25 (4) (2009) 931-938 14 Lakestani, M., Dehghan, M., Numerical solution of Fokker-planck equation using the cubic B-spline scaling functions Numerical Methods