General framework, stability and error analysis for numerical stiff boundary value methods
From MaRDI portal
Publication:1116664
DOI10.1007/BF01396767zbMath0666.65056MaRDI QIDQ1116664
Uri M. Ascher, Robert M. M. Mattheij
Publication date: 1988
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/133323
global stabilityerror analysisstiff equationsturning pointinternal layersmultiple shootingsymmetric difference schemesone-sided difference schemes
Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)
Related Items
A polyvalent Runge-Kutta triple, An approximate solution for homogeneous boundary-value problems with slowly-varying coefficient matrices, High-order multistep methods for boundary value problems, A new mesh selection strategy for ODEs, Comments on BVPs in non-Newtonian boundary-layer flow, Convergence and instability in PCG methods for bordered systems, A posteriori error estimation for elasto-plastic problems based on duality theory, High-order transverse schemes for the numerical solution of PDEs, Nonlinear numerics, Collocation in space and time: Experience with the Korteweg-de Vries equation, Approximating and computing nonlinear matrix differential models, The application of explicit Nyström methods to singular second order differential equations, Multiple shooting with dichotomically stable formulae for linear boundary-value problems, Upper and lower error estimation for the Tau method and related polynomial techniques, Numerical methods for three-dimensional models of the urine concentrating mechanism, Turnpikes and computation of piecewise open-loop equilibria in stochastic differential games, Adaptive local overlapping grid methods for parabolic systems in two space dimensions, RWPKV: A software package for continuation and bifurcation problems in two-point boundary value problems, Numerical solutions of matrix differential models using cubic matrix splines. II, Least-squares collocation for linear higher-index differential-algebraic equations, On the solvability of two-point, second-order boundary value problems, Perturbation bounds for matrix square roots and Pythagorean sums, Parallel quasi-Newton techniques with applications to shooting methods, Error control for initial value problems with discontinuities and delays, On shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions, Defect-controlled numerical methods and shadowing for chaotic differential equations, The tolerance proportionality of adaptive ODE solvers, Improving the efficiency of the multiple shooting technique, Blending curves for landing problems by numerical differential equations. III: Separation techniques, On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution, Solving boundary value problems of ordinary differential equations with non-separated boundary conditions, A survey of shadowing methods for numerical solutions of ordinary differential equations, Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity, High-order interpolants for solutionsof two-point boundary value problems using MIRK methods, The periodic QR algorithm is a disguised QR algorithm, Runge-Kutta methods for the solution of stiff two-point boundary value problems, Long-term dynamics of nonlinear MDOF engineering systems, On parallel methods for boundary value ODEs, Conditions and conditioning, stability and stabilization, Blending curves for landing problems by numerical differential equations. II: Numerical methods, Improved error bounds for freezing solutions of linear boundary value problems, Probabilistic analysis on the splitting-shooting method for image transformations, Spline based computational technique for linear singularly perturbed boundary value problems, One-way large range step methods for Helmholtz waveguides, RWPM: A software package of shooting methods for nonlinear two-point boundary value problems, Shadows, chaos, and saddles, A survey of numerical techniques for solving singularly perturbed ordinary differential equations, Blending curves for landing problems by numerical differential equations. I: Mathematical modelling, A spline method for second-order singularly perturbed boundary-value problems, Parallel stable compactification for ODEs with parameters and multipoint conditions, An approximate solution for linear boundary-value problems with slowly varying coefficients, Numerical multisteps matrix methods for \(Y=f(t,Y)\), Numerical solution of matrix differential models using cubic matrix splines, Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An automatic orthonormalization method for solving stiff boundary-value problems
- On some difference schemes for singular singularly-perturbed boundary value problems
- Continuous orthonormalization for boundary value problems
- Dichotomies in stability theory
- An Analysis of the Box and Trapezoidal Schemes for Linear Singularly Perturbed Boundary Value Problems
- Collocation for Singular Perturbation Problems II: Linear First Order Systems Without Turning Points
- Collocation for Singular Perturbation Problems I: First Order Systems with Constant Coefficients
- Numerical Methods for Stiff Two-Point Boundary Value Problems
- On Dichotomy and Well Conditioning in BVP
- A High-Order Method for Stiff Boundary Value Problems with Turning Points
- Decoupling and Stability of Algorithms for Boundary Value Problems
- Collocation Software for Boundary-Value ODEs
- On Collocation Implementation for Singularly Perturbed Two-Point Problems