Parabolic Problems

  • Granville Sewell

Abstract

The form of the time-dependent PDE system solved by PDE/PROTRAN (Section 1.5) is:
$$\begin{array}{*{20}{c}} {C(x,y,t,u){u_t}) = {A_x}(x,y,u,{u_x},{u_y}) + {B_y}(x,y,t,u,{u_x},{u_y}) + F(x,y,t,u,{u_x},{u_y})\,in\,R} \\ {u = FB(x,y,t)\,on\,\partial {R_1}} \\ {A{n_x} + B{n_y} = GB(x,y,t,u)\,on\,\partial {R_2}} \\ {u = UO(x,y)\,at\,t = {t_0}} \end{array}$$
(4.1.1)
where R is a general two dimesional region, \(\partial {R_1}\,and\,\partial {R_2}\) are disjoint parts of the boundary, and C is a diagonal m by m matrix (m=number of PDEs).

Keywords

Assure 

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References

  1. 1.
    Forsythe, G.E., Wasow, W.R., Finite Difference Methods for Partial Differential Equations, John Wiley and Sons, New York (1960).MATHGoogle Scholar
  2. 2.
    Mitchell, A. R., Griffiths, D. F., The Finite Difference Method in Partial Differential Equations, John Wiley and Sons, New York, (1980).MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Granville Sewell
    • 1
  1. 1.Mathematics DepartmentUniversity of Texas at El PasoEl PasoUSA

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