Solution of nonlinear boundary value problems—X: The false transient method

The solution of a nonlinear boundary value problem may be found by solving a pertinent transient equation until the solution ceases to change significantly (the false transient method). The method is used to get a solution of a strongly nonlinear diffusion problem as well as towards solution of equations arising in the boundary layer theory. If multiple solutions occur the false transient method is not capable of calculating all profiles. For the boundary layer problems it is difficult to construct a reliable false transient equation if it is not based on a physically “sound” transient model.