Three-point backward finite-difference method for solving a system of mixed hyperbolic—parabolic partial differential equations

• Published in: Computers & chemical engineering 1990, Vol.14 (6), p.679-685
• Main Authors: Wu, J.C., Fan, L.T., Erickson, L.E.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, miscellaneous problems; Sciences and techniques of general use
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/0098-1354(90)87036-O

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.