Gas flow problem: solving non-linear BVP with given lower-upper solutions interactively

Abstract

Modelling the unsteady isothermal flow of a gas through a semi-infinite porous medium results in a sensitive non-linear two-point boundary value problem (BVP) over an infinite interval for which the lower and upper solutions have been established analytically. We present an interactive solution procedure based on the lower and upper solutions (LUSOL) for this BVP whose conversion to an initial value problem (IVP) without making use of the LUSOL is usually not numerically possible. In other words, the gas flow problem considered here is an excellent example of a case where knowledge of easily computable LUSOL is extremely important if one does not want to land in a situation in which all non-LUSOL-based methods fail.

Keywords:

• Finite-difference scheme
• Gas flow
• Interactive solution procedure
• Interpolation
• Lower and upper solutions
• Mean-value theorem
• Non-linear boundary value problem