A stepsize control for continuation methods and its special application to multiple shooting techniques

DOI10.1007/BF01399549zbMath0428.65032MaRDI QIDQ1137353

Peter Deuflhard

Publication date: 1979

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132632

zbMATH Keywords

predictorstwo-point boundary value problemscorrectorNewton-Kantorovich theoremhomotopy problemshootingdamped Newton methodaffine invariant convergence theorem

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory ⋮ The grand four: affine invariant globalizations of Newton's method ⋮ Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface ⋮ Updated projections in continuation methods ⋮ Numerical differentiation of implicitly defined space curves ⋮ Adaptive continuation algorithms with application to combustion problems ⋮ Enlarging the domain of convergence for multiple shooting by the homotopy method ⋮ Solving boundary-value problems with a spline-collocation code ⋮ On rank-deficient pseudoinverses ⋮ Affine invariant convergence results for Newton's method ⋮ Variable Schrittweitensteuerungen für die Homotopiemethode bei adäquaten nichtlinearen Ausgleichsproblemen ⋮ Following paths through turning points ⋮ Secant methods for sparse systems of nonlinear equations with a special structure ⋮ Mixed precision path tracking for polynomial homotopy continuation ⋮ On the solution of highly structured nonlinear equations ⋮ On the radius of convergence of newton's method ⋮ Numerical continuation through folds with step control ⋮ Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography ⋮ Gauss pseudospectral and continuation methods for solving two-point boundary value problems in optimal control theory ⋮ Bifurcations in parametric nonlinear programming ⋮ POMULT: A program for computing periodic orbits in Hamiltonian systems based on multiple shooting algorithms ⋮ On accelerating PL continuation algorithms by predictor—corrector methods ⋮ Branch switching in bifurcation problems for ordinary differential equations ⋮ A note on the solution to a common thermal network problem encountered in heat-transfer analysis of spacecraft ⋮ Numerical identification of selected rate constants in large chemical reaction systems ⋮ The solution of multi-parameter systems of equations with application to problems in nonlinear elasticity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Taylor series method for the numerical solution of two-point boundary value problems
• Iterative continuation and the solution of nonlinear two-point boundary value problems
• Optimization and optimal control. Proceedings of a conference held at Oberwolfach, November 17-23, 1974
• A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
• Numerical solution of the singular Ginzburg-Landau equations by multiple shooting
• Über einen Ordnungsbegriff bei Einbettungsalgorithmen zur Lösung nichtlinearer Gleichungen
• A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques
• Comparing routines for the numerical solution of initial value problems of ordinary differential equations in multiple shooting
• Numerical treatment of ordinary differential equations by extrapolation methods
• On shooting methods for boundary value problems
• Ein Iterationsverfahren zur Lösung spezieller nichtlinearer Randwertprobleme
• Numerische Aspekte bei der Einbettung nichtlinearer Probleme
• Solution of Troesch's, and other, two point boundary value problems by shooting techniques
• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Automatische Schrittweitensteuerung bei global konvergenten Einbettungsmethoden
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• On the Stability Problem for Shallow Spherical Shells
• Local Mapping Relations and Global Implicit Function Theorems
• The continuation method for functional equations