FDM for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations

A finite difference method (FDM) for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations is studied. Nonlinear coupled property is fully considered. Variant techniques of discrete functional analysis such as summation by parts and deductive reasoning are used to make prior estimates. The FD scheme is uniquely solvable and unconditionally stable. With the approximation property of the scheme, the convergence is obtained with a rate of O ( h 2 + Δ t 2 ) order.