Application of the Crank–Nicolson time integrator to viscoelastic wave equations with boundary feedback damping. (14th October 2020)

• Record Type: Journal Article
• Authors: Xu, Da
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 1(2022)
• Page Start: 487
• Page End: 514
• Publication Date: 2020-10-14
• Subjects: boundary feedback damping -- viscoelasticity -- Crank–Nicolson method -- l2stability -- uniform convergence; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa071
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We study the numerical solutions for a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod. The problem is discretized by the Crank–Nicolson scheme based on the trapezoidal rule: while the time derivative is approximated by the trapezoidal rule in a two-step way, a convolution quadrature formula, constructed again from the trapezoidal rule, is used to approximate the integral term. Error estimates of the numerical scheme are derived in the $ l^{\infty }_{t}(0, ~\infty ;~L^{2}(0, ~1)) $ norm. Results from some numerical experiment are presented.