A method of directly defining the inverse mapping for solutions of non-linear coupled systems arising in convection heat transfer in a second grade fluid

摘要

In this paper, we extend Liao’s newly invented Directly Defining inverse Mapping Method (MDDiM) to obtain solutions to fourth order nonlinear systems arising in combined free and forced convection flow of a second-grade fluid, over a stretching sheet. Errors ranging from 10−5 to 10−9 are reported for a relatively few terms. The idea is novel and this is the first time MDDiM has been used for a fourth-order coupled system. So, this idea is not limited to a single equation, but can also be used for coupled equations. The same idea could be applied to systems of several equations, etc. Also, it is important to note that finding an inverse linear operator that works well (gives low error, or leads to easily generated solution terms, or both) for a specific type of problem would be worth investigating.