Performance Evaluation of an Extrapolation Method for Ordinary Differential Equations with Error-free Transformation
It offers a computationally efficient alternative for solving ill-conditioned ODEs, but the improvement is incremental and domain-specific.
The paper applies error-free transformation to explicit extrapolation methods for solving ODEs, achieving effectiveness for large linear and small nonlinear ODEs, particularly with harmonic sequences.
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied by using functions supported by a well-tuned BLAS library. In this paper, we propose the application of EFT to explicit extrapolation methods to solve initial value problems of ordinary differential equations. Consequently, our implemented routines can be effective for large-sized linear ODE and small-sized nonlinear ODE, especially in the case when harmonic sequence is used.