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- Title
Numerical results for a fourth‐order nonlinear wave equation of Kirchhoff type with a viscoelastic term.
- Authors
Thanh, Le Thi Mai; Dung, Tran Trinh Manh; Nhan, Nguyen Huu; Ngoc, Le Thi Phuong; Long, Nguyen Thanh
- Abstract
In this paper, numerical results for a fourth‐order nonlinear wave equation of Kirchhoff type with a viscoelastic term are established. First, the existence and uniqueness of a solution is proved by applying the Faedo–Galerkin method and the weak compact method. Next, an algorithm to the initial boundary value problem for a nonlinear evolution equation of fourth order is studied where the spatial‐variable discretization and time‐variable discretization are constructed to approximate derivatives by the difference schemes. Finally, the numerical results are shown to present the errors of proposed algorithm. Simulations of the approximate solution and the exact solution are also visualized.
- Subjects
NONLINEAR wave equations; NONLINEAR boundary value problems; WAVE equation; INITIAL value problems; NONLINEAR evolution equations; NONLINEAR difference equations
- Publication
Numerical Methods for Partial Differential Equations, 2022, Vol 38, Issue 5, p1319
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22837