Computing positive fixed-points of decreasing Hammerstein operators by relaxed iterations

DOI10.1216/jiea/1020282136zbMath0979.65047OpenAlexW2066610155MaRDI QIDQ5939756

Alvise Sommariva, Marco Vianello

Publication date: 30 July 2001

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/jie/VOL12-1/CONT12-1/CONT12-1.html

zbMATH Keywords

global convergenceconepositive solutionradiative transferJacobi methodNewton-type methodsabstract nonlinear operator equationsatmospheric heat transferChandrasekhars \(H\)-equationcompletely continuous operatorfixed-point equationGauss-Seidel methodsHammerstein equationNemytskij operatornuclear physicsordered Banach spacesPicard-like iterationstationary underrelaxation

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear parabolic equations (35K55) Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Fixed-point theorems (47H10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical solutions to equations with nonlinear operators (65J15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items

Model of neo-Malthusian population anticipating future changes in resources ⋮ A Fixed Point Theorem for Decreasing Functions ⋮ Cost effectiveness and policy announcement: the case of measles mandatory vaccination

Uses Software

• KELLEY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of a nonlinear integral equation arising in particle transport theory
• A survey of numerical methods for solving nonlinear integral equations
• Positive solutions of a class of nonlinear integral equations and applications
• On certain nonlinear integral equations
• Positive fixed points and eigenvectors of noncompact decreasing operators with applications to nonlinear integral equations
• Constructive approximation for a class of perturbed Hammerstein integral equations
• Positive solutions of a non-linear integral equation
• An equation of Hammerstein type arising in particle transport theory
• A Mesh-Independence Principle for Operator Equations and Their Discretizations
• Coupled fixed points of nonlinear operators with applications
• A New Approach to the H-Equation of Chandrasekhar
• Approximating fixed-points of decreasing operators in spaces of continuous functions^*
• Existence and uniqueness of positive fixed points for mixed monotone operators and applications
• Multiple positive solutions on nonlinear integral equations and applications
• Constructive analysis of purely integral Boltzmann models