Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations

• Published in: Advances in computational mathematics Vol. 47; no. 1
• Main Authors: Wang, Wansheng, Mao, Mengli, Wang, Zheng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2021; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Errors; Estimates; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Norms; Stability; Upper bounds; Visualization; 65M15; Linear parabolic equations; 65L06; 65J08; Error estimates; Stability; Variable step-size BDF2 method; Semilinear parabolic equations; 65M12
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-020-09839-2

In this paper, stability and error estimates for time discretizations of linear and semilinear parabolic equations by the two-step backward differentiation formula (BDF2) method with variable step-sizes are derived. An affirmative answer is provided to the question: whether the upper bound of step-s...