Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms

In this piece of work, we introduce a new idea and obtain stability interval for explicit difference schemes of O(k2+h2) for one, two and three space dimensional second-order hyperbolic equations utt=a(x,t)uxx+α(x,t)ux-2η2(x,t)u,utt=a(x,y,t)uxx+b(x,y,t)uyy+α(x,y,t)ux+β(x,y,t)uy-2η2(x,y,t)u, and utt=a(x,y,z,t)uxx+b(x,y,z,t)uyy+c(x,y,z,t)uzz+α(x,y,z,t)ux+β(x,y,z,t)uy+γ(x,y,z,t)uz-2η2(x,y,z,t)u,00 subject to appropriate initial and Dirichlet boundary conditions, where h>0 and k>0 are grid sizes in space and time coordinates, respectively. A new idea is also introduced to obtain explicit difference schemes of O(k2) in order to obtain numerical solution of u at first time step in a different manner.