Achieving tolerance proportionality in software for stiff initial-value problems
Copyright policy )Achieving tolerance proportionality in software for stiff initial-value problems
The paper presents a basis for a uniform interpretation of the user's accuracy requirement in codes for solving stiff initial value problems. It is shown that it is possible to design the local error control strategy in a code in such a way as to achieve the tolerance proportionality. The strategy is based on a control of the local error per unit step. Next, the strategy is discussed for two stiff solvers: LSODE (Hindmarsh, 1980) and SECDER (Addison, 1979). The numerical results show that the strategy leads to a significant improvement in tolerance proportionality at litte extra cost.
- University of Waterloo Canada
- University of Toronto Canada
stiff initial value problems, LSODE, local extrapolation, Mesh generation, refinement, and adaptive methods for ordinary differential equations, tolerance proportionality, Software, source code, etc. for problems pertaining to ordinary differential equations, Nonlinear ordinary differential equations and systems, SECDER, Numerical methods for initial value problems involving ordinary differential equations, local error control strategy
stiff initial value problems, LSODE, local extrapolation, Mesh generation, refinement, and adaptive methods for ordinary differential equations, tolerance proportionality, Software, source code, etc. for problems pertaining to ordinary differential equations, Nonlinear ordinary differential equations and systems, SECDER, Numerical methods for initial value problems involving ordinary differential equations, local error control strategy
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