**6. Conclusions**

In this study, we present new scheme using CBS of some non-linear differential equations arising in visco-elastic flows and hydrodynamic stability problems. The proper selection for the choice of the scheme and an appropriate of adjustment BCs may cause elasticity for the betterment of the results. The new CBS scheme proposed in this study is very simple to apply in solving the non-linear DEs compared with some existing schemes. An advantage of using the CBS scheme is that it gives a spline function on each new time line which can be applied to achieve the numerical solutions at any stage in the space direction.

**Author Contributions:** Conceptualization, A.T., A.G. and A.K.; methodology, A.T., A.K. and M.N.N.; software, A.T., A.K., F.K. and K.S.N; formal analysis, S.A.A.K., K.S.N. and F.K.; writing-original draft preparation, A.K., A.G. and S.A.A.K.; writing-review and editing, A.T., K.S.N. and A.G.; visualization, F.K., M.N.N. and A.G.; supervision, M.N.N. and S.A.A.K.; funding acquisition, A.T.

**Funding:** This research is funded by Deanship of Scientific Research at Majmaah University, Project Number (R-1441-25).

**Acknowledgments:** The first author Asifa Tassaddiq (A.T) would like to thank Deanship of Scientific Research at Majmaah University, for supporting this work under Project Number (R-1441-25).

**Conflicts of Interest:** The authors declare no conflict of interest.
