On solving a special class of weakly nonlinear finite-difference systems

DOI10.1080/00207160701650353zbMath1177.65165OpenAlexW1970387561MaRDI QIDQ3615554

Emanuele Galligani

Publication date: 20 March 2009

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701650353

zbMATH Keywords

numerical experimentsconvection-diffusion problemsfinite differenceinexact Newton methodweakly nonlinear systemsline search techniqueNewton-iterative method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (3)

On the solution of a class of nonlinear systems governed by an \(M\)-matrix ⋮ Lagged diffusivity fixed point iteration for solving steady-state reaction diffusion problems ⋮ The arithmetic mean method for solving systems of nonlinear equations in finite differences

Uses Software

• NewtonLib
• KELLEY

Cites Work

• Affine invariant convergence results for Newton's method
• A parallel algorithm for solving block tridiagonal linear systems
• The two-stage arithmetic mean method
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
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• On the Newton interior-point method for nonlinear programming problems
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• Local Convergence of Inexact Newton Methods
• Group explicit iterative methods for solving large linear systems
• Multi-Splittings of Matrices and Parallel Solution of Linear Systems
• The Solution of Two-Point Boundary Value Problems by the Alternating Group Explicit (AGE) Method
• On Steplength Algorithms for a Class of Continuation Methods
• Inexact Newton Methods
• Asymptotic Mesh Independence of Newton–Galerkin Methods via a Refined Mysovskii Theorem
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Numerical Optimization
• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems
• Globally Convergent Inexact Newton Methods
• Choosing the Forcing Terms in an Inexact Newton Method
• Convergence Conditions for Ascent Methods
• Convergence Conditions for Ascent Methods. II: Some Corrections
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