Abstract
Through the current article, a numerical technique to obtain an approximate solution of one-dimensional linear hyperbolic partial differential equations is implemented. A certain combination of the shifted Chebyshev polynomials of the fifth-kind is used as basis functions. The main idea behind the proposed technique is established on converting the governed boundary-value problem into a system of linear algebraic equations via the application of the spectral Galerkin method. The resulting linear system can be solved by expedients of the Gaussian elimination procedure. The convergence and error analysis of the shifted Chebyshev expansion are carefully investigated. Various numerical examples are given to demonstrate the power and accuracy of the given method.
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