Abstract
Modeling an infinite domain arises while simulating physical applications frequently. It is like attempting to model the effects and properties of the ocean in a bucket. In this paper, we develop a spectral Galerkin method based on exponential Jacobi functions (EJF) in unbounded domains. We also establish some basic results on exponential Jacobi orthogonal approximations, which serve as the mathematical foundation of spectral methods for various partial differential equations in unbounded domains. We derive the exponential Lagrange interpolation formula and its related error estimates. As examples, hyperbolic partial differential equations in multidimensions are considered. Related spectral Galerkin schemes are proposed. The test and trial function spaces are carefully chosen to obtain desired convergence properties. Through three examples, we demonstrate that the proposed method yields highly accurate results.
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