Numerical analysis and simulation for a nonlinear wave equation

In this work we study a nonlinear wave equation, depending on different norms of the initial conditions, has bounded solution for all t>0t>0 or 00T0>0. We also prove that the solution may blow-up at T0T0. 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∗,t∗), where the blow-up occurs for different ρρ values in a numerical simulation.