Work

Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation

Year: 2023

Type: article

Abstract: A variable-step BDF2 time-stepping method is investigated for simulating the extended Fisher-Kolmogorov equation. The time-stepping scheme is shown to preserve a discrete energy dissipation law if the adjacent time-step ratios r n ≔ Τ n / Τ n − 1 < 3 + 17 / 2 ≈ 3.561 . With the aid of discrete orthogonal convolution kernels, concise L 2 norm error estimates are proved, for the first time, under the mild step ratios constraint 0 < r n < 3.561 . Our error estimates are almost independent of the step ratios r n so that the proposed numerical scheme is robust with respect to the variations of time steps. An adaptive time-stepping strategy based on solution accuracy is then applied to update the computational efficiency. Numerical examples are included to illustrate our theoretical results.

Source: Journal of Function Spaces

DOI: 10.1155/2023/1869660

Authors: Yang Li, Qihang Sun, Naidan Feng, Jianjun Liu

Institutions: Shanghai University, Shandong University of Science and Technology, Ludong University, Nanjing University of Aeronautics and Astronautics

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,375

Funders: National Natural Science Foundation of China, Natural Science Foundation of Liaoning Province, Higher Education Discipline Innovation Project