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Exponential Jacobi spectral method for hyperbolic partial differential equations. (English) Zbl 1452.35088

Summary: Herein, we have proposed a scheme for numerically solving hyperbolic partial differential equations (HPDEs) with given initial conditions. The operational matrix of differentiation for exponential Jacobi functions was derived, and then a collocation method was used to transform the given HPDE into a linear system of equations. The preferences of using the exponential Jacobi spectral collocation method over other techniques were discussed. The convergence and error analyses were discussed in detail. The validity and accuracy of the proposed method are investigated and checked through numerical experiments.

MSC:

35L04 Initial-boundary value problems for first-order hyperbolic equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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