Research Article
Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values
@INPROCEEDINGS{10.1007/978-3-030-92942-8_17, author={Pham Nguyen Nhat Khanh and Le Thi Mai Thanh and Tran Trinh Manh Dung and Nguyen Huu Nhan}, title={Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values}, proceedings={Nature of Computation and Communication. 7th EAI International Conference, ICTCC 2021, Virtual Event, October 28--29, 2021, Proceedings}, proceedings_a={ICTCC}, year={2022}, month={1}, keywords={Nonlinear wave equation High-order iterative scheme 2-order iterative scheme Finite-difference scheme Numerical results 35L20 35L70 35Q72}, doi={10.1007/978-3-030-92942-8_17} }- Pham Nguyen Nhat Khanh
Le Thi Mai Thanh
Tran Trinh Manh Dung
Nguyen Huu Nhan
Year: 2022
Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values
ICTCC
Springer
DOI: 10.1007/978-3-030-92942-8_17
Abstract
In the present paper, we consider an initial-boundary value problem for nonlinear equation in which the source term contains two boundary values. First, the local existence and uniqueness of a weak solution to this problem is inferred directly from [12], in which a recurrent sequence via aN-order iterative scheme is established and then theN-order convergent rate of the sequence to the unique weak solution of the proposed model is also proved. As(N=2), the corresponding scheme called 2-order iterative scheme is considered, and a numerical algorithm to calculate approximate solutions via the 2-order iterative scheme is constructed by the finite-difference method. Finally, a numerical example is presented to evaluate the errors between the exact solution and the approximate solution. The numerical results show that the errors are decreasing as the fineness of meshes is increasing.
