Construction of variable-stepsize multistep formulas
Mathematics of Computation
Computer-controlled systems: theory and design (2nd ed.)
Computer-controlled systems: theory and design (2nd ed.)
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
Control Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers
SIAM Journal on Scientific Computing
Numerical Computation, Volume I
Numerical Computation, Volume I
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
A collocation formulation of multistep methods for variable step-size extensions
Applied Numerical Mathematics
Digital filters in adaptive time-stepping
ACM Transactions on Mathematical Software (TOMS)
Time-step selection algorithms: adaptivity, control, and signal processing
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Constant coefficient linear multistep methods with step density control
Journal of Computational and Applied Mathematics
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We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of DASSL and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of DASSL are therefore much greater than the standard implementation seems to suggest.