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FDM for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations. (English) Zbl 1081.65087
The authors develop a finite difference method (FDM) for a multi-dimensional coupled system of nonlinear parabolic and hyperbolic equations and prove the existence, stability and uniqueness of its solution by a set of theorems. Finally, the proposed method is illustrated by a number of numerical experiments.

##### MSC:
 65M06 Finite difference methods (IVP of PDE) 35M10 PDE of mixed type 65M12 Stability and convergence of numerical methods (IVP of PDE) 35K55 Nonlinear parabolic equations 35L70 Nonlinear second-order hyperbolic equations
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