Parameter optimization in the regularized Shannon's kernels of higher‐order discrete singular convolutions
Copyright policy )Parameter optimization in the regularized Shannon's kernels of higher‐order discrete singular convolutions
AbstractThe δ‐type discrete singular convolution (DSC) algorithm has recently been proposed and applied to solve kinds of partial differential equations (PDEs). With appropriate parameters, particularly the key parameter r in its regularized Shannon's kernel, the DSC algorithm can be more accurate than the pseudospectral method. However, it was previously selected empirically or under constrained inequalities without optimization. In this paper, we present a new energy‐minimization method to optimize r for higher‐order DSC algorithms. Objective functions are proposed for the DSC algorithm for numerical differentiators of any differential order with any discrete convolution width. Typical optimal parameters are also shown. The validity of the proposed method as well as the resulted optimal parameters have been verified by extensive examples. Copyright © 2003 John Wiley & Sons, Ltd.
- Singapore Management University Singapore
- National University of Singapore Singapore
- National University of Singapore Libraries Singapore
Regularized Shannon's kernels, 510, Navier-Stokes equation, Physical Sciences and Mathematics, Numerical differentiators, Objective functions, regularized Shannon's kernels, numerical examples, algorithm, finite difference method in space, pseudospectral method, parameter optimization energy minimization, 620, Energy minimization, discrete singular convolutions, Parameter optimization, Boundary value problems for higher-order elliptic equations, numerical differentiators, objective functions, Discrete singular convolutions, Spectral, collocation and related methods for boundary value problems involving PDEs, Navier-Stokes equations, Runge-Kutta method in time, Kirchhoff plate vibration, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Regularized Shannon's kernels, 510, Navier-Stokes equation, Physical Sciences and Mathematics, Numerical differentiators, Objective functions, regularized Shannon's kernels, numerical examples, algorithm, finite difference method in space, pseudospectral method, parameter optimization energy minimization, 620, Energy minimization, discrete singular convolutions, Parameter optimization, Boundary value problems for higher-order elliptic equations, numerical differentiators, objective functions, Discrete singular convolutions, Spectral, collocation and related methods for boundary value problems involving PDEs, Navier-Stokes equations, Runge-Kutta method in time, Kirchhoff plate vibration, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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