Numerical analysis and simulation for a nonlinear wave equation

详细信息    查看全文

• 作者：M.A. Rincon^a ; ^{rincon@dcc.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; N.P. Quintino^b ; ^{natanael.quintino@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35L70 ; 65M12 ; 65M60
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：247-264
• 全文大小：812 K

文摘

In this work we study a nonlinear wave equation, depending on different norms of the initial conditions, has bounded solution for all t>0$t>0$ or 0<t<T₀$0<t<T_0$ for some T₀>0$T_0>0$. We also prove that the solution may blow-up at T₀$T_0$. Proofs of some the analytical results listed are sketched or given. For approximate numerical solutions we use the finite element method in the spatial variable and the finite difference method in time. The nonlinear system for each time step is solved by Newton’s modified method. We present numerical analysis for error estimates and numerical simulations to illustrate the convergence of the theoretical results. We present too, the singularity points $(x^{\ast },t^{\ast })$, where the blow-up occurs for different ρ$\rho$ values in a numerical simulation.