In this paper, we propose mixed generalized Hermite-Legendre spectral method for partial differential equation set in an infinite strip. We investigate mixed generalized Hermite-Legendre approximation. We propose the new algorithm for various boundary condition problems with variable coefficient. The global convergence of proposed algorithms is proved. Numerical results demonstrate the spectral...

The authors of [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 6634–6639] proposed sparse Fourier domain approximation of solutions to multiscale PDE problems by soft thresholding. We show here that the method enjoys a number of desirable numerical and analytic properties, including convergence for linear PDEs and a modified equation resulting from the sparse approximation. We also extend the meth...

seismic waves are non-stationary due to its propagation through the earth. time-frequency transformsare suitable tools for analyzing non-stationary seismic signals. spectral decomposition can reveal thenon-stationary characteristics which cannot be easily observed in the time or frequency representationalone. various types of spectral decomposition methods have been introduced by some researche...