Stability and Convergence of Approximate Solutions to the Moore-Gibson-Thompson Equation

We study the formulation of two approximation schemes for the solutions of a particular partial differential equation, the Moore-Gibson-Thompson equation, arising in nonlinear acoustics. The established theory of well posedness for the linear and nonlinear equation is summarized, and then the main results of the work are the time-stability of the approximate solutions by either scheme, and the convergence of the approximations to the original solution with explicit rates of convergence provided.