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Stable explicit difference approximations to parabolic partial differential equations
Author(s) -
Liu SheanLin
Publication year - 1969
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690150308
Subject(s) - mathematics , parabolic partial differential equation , partial differential equation , nonlinear system , mathematical analysis , neumann boundary condition , method of lines , boundary value problem , numerical partial differential equations , finite difference method , elliptic partial differential equation , method of characteristics , ftcs scheme , finite difference , differential equation , differential algebraic equation , ordinary differential equation , physics , quantum mechanics
A finite‐difference method is developed for numerical solution of parabolic partial differential equations. This technique is explicit and stable. It is shown that the present method is more accurate and faster, in terms of computer time, than the Crank‐Nicholson method. A method of handling nonlinear problems is also presented. Two examples are given to illustrate the present technique. The first problem is a linear diffusion equation. The second problem deals with two simultaneous nonlinear parabolic partial differential equations with Neumann boundary conditions describing the steady state of a packed‐bed catalytic reactor with radial mixing.