article

PLTMGC

Authors:

Randolph E. Bank,

Tony F. ChanAuthors Info & Claims

SIAM Journal on Scientific and Statistical Computing, Volume 7, Issue 2

Pages 540 - 559

https://doi.org/10.1137/0907036

Published: 01 April 1986 Publication History

Abstract

PLTMGC is a program package for solving nonlinear elliptic systems that have explicit dependence on a scalar parameter. In addition to being able to compute solutions for fixed parameter values, it can be used to solve the linear eigenvalue problem, trace solution branches, locate singular points (simpleturning points and bifurcation points) and switch branch at simple bifurcation points. A multi-grid continuation approach is employed in which a continuation procedure is used to follow the solution curve on the coarsest grid and a multi-grid algorithm is used to refine the solution at selected points using an adaptive mesh refinement strategy. Some numerical examples illustrating the performance of the package are given.

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Mohsen A(2014)A simple solution of the Bratu problemComputers & Mathematics with Applications10.1016/j.camwa.2013.10.00367:1(26-33)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.camwa.2013.10.003
Chang SChien CJeng B(2007)An efficient algorithm for the Schrödinger-Poisson eigenvalue problemJournal of Computational and Applied Mathematics10.1016/j.cam.2006.05.013205:1(509-532)Online publication date: 1-Aug-2007
https://dl.acm.org/doi/10.1016/j.cam.2006.05.013
Chien CJeng B(2006)A Two-Grid Discretization Scheme for Semilinear Elliptic Eigenvalue ProblemsSIAM Journal on Scientific Computing10.1137/03060244727:4(1287-1304)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.1137/030602447
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cover image SIAM Journal on Scientific and Statistical Computing

SIAM Journal on Scientific and Statistical Computing Volume 7, Issue 2

1986

355 pages

ISSN:0196-5204

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 April 1986

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Mohsen A(2014)A simple solution of the Bratu problemComputers & Mathematics with Applications10.1016/j.camwa.2013.10.00367:1(26-33)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.camwa.2013.10.003
Chang SChien CJeng B(2007)An efficient algorithm for the Schrödinger-Poisson eigenvalue problemJournal of Computational and Applied Mathematics10.1016/j.cam.2006.05.013205:1(509-532)Online publication date: 1-Aug-2007
https://dl.acm.org/doi/10.1016/j.cam.2006.05.013
Chien CJeng B(2006)A Two-Grid Discretization Scheme for Semilinear Elliptic Eigenvalue ProblemsSIAM Journal on Scientific Computing10.1137/03060244727:4(1287-1304)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.1137/030602447
García-Archilla BSánchez JSimó C(2006)Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations BIT10.1007/s10543-006-0101-046:4(731-757)Online publication date: 1-Dec-2006
https://dl.acm.org/doi/10.1007/s10543-006-0101-0
Boyd J(1996)Numerical Computations of a Nearly Singular Nonlinear EquationJournal of Computational Physics10.1006/jcph.1996.0044124:1(55-70)Online publication date: 1-Mar-1996
https://dl.acm.org/doi/10.1006/jcph.1996.0044

Abstract

Cited By

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A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation

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