The Effect of Variable Mesh Size on the Stability of Multistep Methods

DOI10.1137/0711079zbMath0292.65041OpenAlexW1977638711MaRDI QIDQ4044077

Publication date: 1974

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2027/uiuo.ark:/13960/t3dz1n819

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical analysis in abstract spaces (65J99)

Related Items

Linearly Implicit Multistep Methods for Time Integration, On the zero-stability of multistep methods on smooth nonuniform grids, Multiderivative variable stepsize variable formula methods, The starting procedure in variable-stepsize variable-order PECE codes, Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems, Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction, Time-integration for ALE simulations of fluid-structure interaction problems: stepsize and order selection based on the BDF, Difference Methods for the Numerical Solution of Time-Varying Singular Systems of Differential Equations, Numerical treatment of large-scale air pollution models, A New Step-Size Changing Technique for Multistep Methods, The second-order backward differentiation formula is unconditionally zero-stable, Advances in the theory of variable stepsize variable formula methods for ordinary differential equations, A variable-step central difference method for structural dynamics analysis. I. Theoretical aspects, Sharp L2 norm convergence of variable-step BDF2 implicit scheme for the extended Fisher-Kolmogorov equation, Second-order time discretization for reaction coefficient estimation of bilinear parabolic optimization problem with Neumann boundary conditions, A new stepsize change technique for Adams methods, On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation, On solving the stiff ODE's of the kinetics of chemically reacting gas flow, Zero-stability properties of the three-ordinate variable stepsize variable formula methods, Variable order Adams codes., Stability of linear multistep methods and applications to nonlinear parabolic problems., The numerical solution of neutral functional differential equations by Adams predictor-corrector methods, Variable step stiffly stable methods, One-step and linear multistep methods for nonlinear consolidation, Unnamed Item, Exponentially fitted variable two-step BDF algorithm for first order ODEs, Nordsieck methods on nonuniform grids: stability and order reduction phenomenon, Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones, Stability properties of variable stepsize variable formula methods, Convergence of multistep methods for Volterra functional differential equations, On the convergence of multistep methods for the Cauchy problem for ordinary differential equations, The continuous extension of the B-spline linear multistep methods for BVPs on non-uniform meshes, Direct time integration methods in nonlinear structural dynamics, Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations, Stability of multistep-methods on variable grids, Elements of a general theory of composite integration methods, Two high-order multistep methods with offstep points applied with a variable stepsize, Computable explicit bounds for the discretization error of variable stepsize multistep methods, Consistency and convergence of general linear multistep variable stepsize variable formula methods, Analysis of adaptive BDF2 scheme for diffusion equations, Variable-step deferred correction methods based on backward differentiation formulae for ordinary differential equations, Variable stepsize variable formula methods based on predictor-corrector schemes, Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems, Automatic integration of Euler-Lagrange equations with constraints, Time-adaptive partitioned method for fluid-structure interaction problems with thick structures, Variable multistep methods for delay differential equations