Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation

DOI10.1017/S1446181100011597zbMath0969.65040OpenAlexW2099089995MaRDI QIDQ4511562

E. Balakrishnan, Adrian Swift

Publication date: 24 June 2001

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181100011597

zbMATH Keywords

multiple solutionsreaction-diffusion equationsystems of nonlinear equationscombustion theorypathfollowing methods

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Combustion (80A25) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Cites Work

• Path-following for disjoint bifurcation problems arising in ignition theory
• Critical values for some non-class \(A\) geometries in thermal ignition theory
• The Pseudo-Spectral Method and Path Following in Reaction-Diffusion Bifurcation Studies
• Comparison of a continuation method with Brent's method for the numerical solution of a single nonlinear equation
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• A New Method of Solving Nonlinear Simultaneous Equations
• A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination
• Some Efficient Algorithms for Solving Systems of Nonlinear Equations

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