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Numerical solution of second order boundary value problem using rational method AIP Conference Proceedings 1682, 020013 (2015) Abstract. An explicit two-step, second order rational method for the numerical solution of first order initial value problems is introduced in this paper. Existing rational multistep methods required the computations of higher derivatives from a given initial value problem. However, the new two-step rational method does not require any computation of these higher derivatives, and thus save up some computational cost. Numerical results showed that the new rational multistep method and existing rational multistep method are found to have comparable accuracy in solving first order initial value problems.

It1 this p;lpcr, a new iniplicit Ilul~gc-Kuttit mclliod \vliicl~ b~lsctl on a 4-point (~; I~I s s -K~~I I~~~I -~~L I~I ; I I I I I clu;~dratu~-c tbnnula is dc\clopcd. The resulting iniplici~ ms~litrd is a 4-stasc sixth ordcr Ga~~ss-Krcr~lrotl-lI:~tl:~~~ Ili\ ~ncthod, or in bricfas C;KKh'l(4.O)-IIA. (;KI)-11A has liighcr s l~g c 01-dcl-.

Hybrid nanofluid is considered a modern and improvised form of nanofluid which usually used to enhance the performance of heat transfer in fluid flow systems. Previous studies found hybrid nanofluid offered a wide range of applications and this opened up numerous new opportunities to further explore the unknown behaviour of hybrid nanofluid under different body geometries and physical parameters. This paper numerically studied a two-dimensional mixed convection and radiative Al2O3-Cu/H2O hybrid nanofluid flow over a vertical exponentially shrinking sheet with partial slip conditions. The main objective is to investigate the effect of mixed convection and radiation on the velocity and temperature profiles, as well as the effect of suction on reduced skin friction and reduced heat transfer with respect to solid volume fraction of copper, velocity, and thermal slips. Exponential similarity variables transformed the governing system of partial differential equations into a system of ordinary differential equations which is solved via MATLAB’s bvp4c solver. Outcomes showed that the value of the reduced heat transfer upsurges in the first solution but declines in the second solution when the velocity slip rises. The reduced heat transfer decreases in both dual solutions when thermal slip is enhanced. As the intensity of thermal slip increases, the reduced skin friction rises in the first solution and decreases in the second. As the mixed convection parameter increases, no obvious variation is noticed in the temperature distribution within the first solution, but increasing trend is observed within the second solution. An increment in the temperature distribution also observed within the dual solutions as the thermal radiation parameter increases. In summary, findings from this study are particularly useful to understand various behaviour of Al2O3-Cu/H2O hybrid nanofluid under the influence of mixed convection, radiation, and partial slip conditions when it flows over a vertical exponential shrinking sheet.

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