A fast Cauchy-Riemann solver-Reference-Cited by-同舟云学术

A fast Cauchy-Riemann solver

Published:1979 Issue:146 Volume:33 Page:585-635
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Ghil Michael,Balgovind Ramesh

Abstract

We present a solution algorithm for a second-order accurate discrete form of the inhomogeneous Cauchy-Riemann equations. The algorithm is comparable in speed and storage requirements with fast Poisson solvers. Error estimates for the discrete approximation of sufficiently smooth solutions of the problem are established; numerical results indicate that second-order accuracy obtains even for solutions which do not have the required smoothness. Different combinations of boundary conditions are considered and suitable modifications of the solution algorithm are described and implemented.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1979-33-146/S0025-5718-1979-0521278-7/S0025-5718-1979-0521278-7.pdf

Reference33 articles.

1. Über die numerische Auflösung von Ranswertproblemen bei elliptischen partiellen Differentialgleichungen;Batschelet, Eduard;Z. Angew. Math. Phys.,1952

2. Approximation of derivatives by finite difference methods in elliptic boundary value problems;Bramble, J. H.;Contributions to Differential Equations,1964

3. A finite difference analogue of the Neumann problem for Poisson’s equation;Bramble, J. H.;J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.,1965

4. O. BUNEMAN, A Compact Non-Iterative Poisson Solver, SUIPR Report No. 294, Inst. Plasma Research, Stanford Univ., May 1969, 11 pp.

5. On direct methods for solving Poisson’s equations;Buzbee, B. L.;SIAM J. Numer. Anal.,1970

Cited by 17 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Vectorial reduced differential transform method for fractional Cauchy–Riemann system of equations;Computational and Mathematical Methods;2021-03-30

2. Formulation and multigrid solution of Cauchy-Riemann optimal control problems;Computing and Visualization in Science;2011-02

3. A full multigrid solution of control-constrained Cauchy–Riemann optimal control problems;Journal of Numerical Mathematics;2011-01

4. The Cauchy-Riemann equations: Discretization by finite elements, fast solution of the second variable, and a posteriori error estimation;Advances in Computational Mathematics;2001

5. Extended Kalman filtering for vortex systems. Part 1: Methodology and point vortices;Dynamics of Atmospheres and Oceans;1998-01