Implementation issues in solving nonlinear equations for two-point boundary value problems

DOI10.1007/BF02250582zbMath0721.65043OpenAlexW120416968MaRDI QIDQ2641087

Margaret H. Wright, Jeff R. Cash

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02250582

zbMATH Keywords

mathematical softwarefinite-difference methodnonlinear algebraic equationsmerit functionsNewton iteration schemewatchdog strategy

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (7)

A new mesh selection strategy for ODEs ⋮ Multiple poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem ⋮ Runge-Kutta methods for the solution of stiff two-point boundary value problems ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ A new algorithm for calculating Adomian polynomials for nonlinear operators ⋮ OPTIMAL FLUCTUATIONS AND THE CONTROL OF CHAOS ⋮ Numerical approximation of nonlinear BVPs by means of BVMs

Uses Software

• COLNEW
• PASVA3
• COLSYS

Cites Work

• A note on solving nonlinear equations and the natural criterion function
• A comparison of some global methods for solving two-point boundary value problems
• Global approximate Newton methods
• High order methods for the numerical solution of two-point boundary value problems
• Iterated deferred corrections for nonlinear boundary value problems
• A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
• A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
• On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae
• Collocation Software for Boundary-Value ODEs
• Parameter Selection for Newton-Like Methods Applicable to Nonlinear Partial Differential Equations
• The watchdog technique for forcing convergence in algorithms for constrained optimization
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• A Variable Order Finite Difference Method for Nonlinear Multipoint Boundary Value Problems
• Comments on the Nature of Automatic Quadrature Routines
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I
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