J. A. Weideman
Abstract
A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.
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Index Terms
- A MATLAB differentiation matrix suite
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Reviews
George K. Adam
The research work presented in this paper tackles the problem of solving differential equations using the spectral collocation method in a software system of 17 MATLAB functions created for this purpose. The algorithms described and the applications examined successfully show the importance of the differentiation matrix suite in the generation of spectral differentiation matrices based on Chebyshev, Fourier, and other interpolants. The algorithms and equations presented are quite significant, solving a variety of problems in scientific computation. The work documents the methods proposed using suitable mathematical terms and equations and sufficient numerical examples to prove its significance. However, further practical cases could have been given in order to justify its intended usage. In general, the length of the work, its presentation, and the references provided are quite sufficient and appropriate. Online Computing Reviews Service
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