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THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)
Citation:
Wu, J. C., L. T. Fan, AND L. E. Erickson. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019). Environmental Progress & Sustainable Energy. American Chemical Society, Washington, DC, 14:679-685, (1990).
Description:
A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differencing to approximate the first-order temporal and spatial derivatives, thereby leading to second-order temporal and spatial accuracy and a substantial reduction in numerical oscillations and diffusion. The resultant finite-difference equations are solved with the tridiagonal matrix method at each time step. For a system of mixed PDEs with coupled nonlinear reaction terms, a two-step expansion technique has been derived to linearize the finite-difference equations and uncouple the PDEs. The accuracy of the expansion is of third-order. Consequently, each PDE can be solved independently with the tridiagonal matrix method. Moreover, the present method can be extended to a system of mixed PDEs coupled with ordinary differential equations and/or algebraic equations.