Discretization and solution of elliptic PDEs-a digital signal processing approach

Article Abstract:

The categories for elliptic partial differential equations (PDEs) are self-adjoint positive definite, indefinite, and nonself-adjoint equations; the difference is in the eigenvalues of the associated differential operator. Using a digital signal processing (DSP) approach to solving elliptic PDEs relies on frequency domain analysis and on multidimensional DSP techniques. Over the last 30 years Fourier analysis has been used more and more to analyze and design numerical PDE algorithms. Using DSP gives numerical analysts a new set of tools to design algorithms and gives electrical engineers a new way to study complex equations.

Algorithms, Numerical analysis, Algorithm, Electrical engineering, Fast Fourier Transforms, Eigenvalue Problems, Partial Differential Equations

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Multidimensional digital signal processing: problems, progress, and future scopes

Article Abstract:

Key mathematical limitations of multidimensional digital signal processing research are highlighted. The settings that facilitate topical investigations are detailed, and the direction of future research is discussed. An increase in techniques for estimating the power spectrum of discrete time deterministic and stochastic processes has been witnessed in the past two decades.

Analysis, Scientific Research, Stochastic Model, Discrete Mathematics

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