Roundoff error problems in interpolation methods for time-fractional problems

Quan，Chaoyu1; Wang，Shijie2; Wu，Xu3

2024-09-01

10.1016/j.apnum.2024.04.008

Applied Numerical Mathematics   影响因子和分区

0168-9274

Roundoff errors often disrupt interpolation methods for time-fractional equations, potentially causing suboptimal convergence or even failure. These issues primarily result from catastrophic cancellations. To address this, we introduce a novel framework for computing coefficients in standard and fast interpolation methods on nonuniform meshes. We propose δ-cancellation and associated threshold conditions to prevent such cancellations. If the thresholds aren't met, a Taylor expansion technique can be applied. Numerical experiments demonstrate our method's accuracy, on par with the Gauss–Kronrod quadrature, but significantly more efficient, allowing for extensive simulations with hundreds of thousands of time steps.

Catastrophic cancellation Roundoff error Sum-of-exponentials approximation Time-fractional problem

SCI ; EI

英语

其他

MATHEMATICS

2-s2.0-85191767165

Scopus

1.School of Science and Engineering,The Chinese University of Hong Kong,Shenzhen,Guangdong,518172,China
2.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Applied Mathematics,The Hong Kong Polytechnic University,Kowloon,Hong Kong

Quan，Chaoyu,Wang，Shijie,Wu，Xu. Roundoff error problems in interpolation methods for time-fractional problems[J]. Applied Numerical Mathematics,2024,203:202-224.

Quan，Chaoyu,Wang，Shijie,&Wu，Xu.(2024).Roundoff error problems in interpolation methods for time-fractional problems.Applied Numerical Mathematics,203,202-224.

Quan，Chaoyu,et al."Roundoff error problems in interpolation methods for time-fractional problems".Applied Numerical Mathematics 203(2024):202-224.