Numerical solution of non-stationary aero-autoelasticity integro-differential operator equations

✍ Scribed by Gamal N. Elnagar; Ahmed Khamayseh

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 123 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(199904)22:6<501::aid-mma47>3.0.co;2-1

✦ Synopsis

The spectral method of G. N. Elnagar, which yields spectral convergence rate for the approximate solutions of Fredholm and Volterra-Hammerstein integral equations, is generalized in order to solve the larger class of integro-differential functional operator equations with spectral accuracy. In order to obtain spectrally accurate solutions, the grids on which the above class of problems is to be solved must also be obtained by spectrally accurate techniques. The proposed method is based on the idea of relating, spectrally constructed, grid points to the structure of projection operators which will be used to approximate the control vector and the associated state vector. These projection operators are spectrally constructed using Chebyshev-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. Simulation studies demonstrate computational advantages relative to other methods in the literature.