Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method

solving two-dimensional fuzzy partial dierential equation by the alternating direction implicit method

solving two-dimensional fuzzy partial dierential equation by the alternating direction implicit method

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Solving Fuzzy Partial Differential Equation by Differential Transformation Method

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Fast wave-front reconstruction by solving the Sylvester equation with the alternating direction implicit method.

Large degree-of-freedom real-time adaptive optics (AO) control requires reconstruction algorithms that are computationally efficient and readily parallelized for hardware implementation. In particular, we find the wave-front reconstruction for the Hudgin and Fried geometry can be cast into a form of the well-known Sylvester equation using the Kronecker product properties of matrices. We derive ...

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is furthe...

Alternating Direction Implicit Method for Two-dimensional Fokker-planck Equation of Dense Spherical Stellar Systems

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum ...