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The aim of this research is to investigate the problem related to the constant accelerated of unsteady MHD third grade fluid in a rotating frame. New numerical approach will be used in order to solve the problem. Hybrid numerical approach of finite difference method and asymptotic interpolation method is introduced. This method is suitable for solving unbounded domain where the domain of the problems tends to infinity. Validation has been made with other analytical method; Homotopy Analysis Method to show that this hybrid method is acceptable. The equation of unsteady state MHD third grade fluid in a rotation about z-axis is derived. The nonlinear equation will be discretized by using finite difference method and couple with asymptotic interpolation to fulfil the unbounded domain of boundary condition. The effect of various values of parameters such as MHD, rotation, time, second and third grade are being tested and discussed. This study concludes that the velocity of distribution decreased when the value of MHD and rotation increased. Meanwhile a contrary result occurs when the factor of time increased. The velocity profile for real part also will be increased and imaginary part will be decreased when the parameter of second and third grade increased.

The aim of this article is to obtain numerical solution for incompressible unsteady flow for third grade fluid induced by variable accelerated plate. Numerical solution is obtained by using Hybrid method which combine between finite difference method (FDM) and asymptotic interpolation method. The influence of difference values of material constant parameters on the velocity flow fluid are discussed and shown graphically.

The aim of this work is to present a suitable numerical solution for unsteady non-Newtonian third-grade fluid which rotates at z -axis and pass through a porous medium. The fluid flows in magnetic field with constant acceleration and the semi-infinite boundary condition are highlighted. The fluid problem is also deal with heat transfer. The nonlinear partial differential equation is discretised using the finite difference method (FDM). The linear system obtained for three different domains (lengths). Consequently, the asymptotic interpolation method is merged to solve problems of large sizes. This hybrid method yielded results that satisfied the boundary condition that reaches zero as length grows to infinite length. For velocity profile and temperature distribution, a comparison of FDM and hybrid method is shown. It is discovered that the hybrid method produces better results than FDM for this infinitely large problem. Several analyses have been carried out to investigate the effect of various fluid parameter values. The findings reveal that as the porosity parameter increases, the velocity decreases. The Grashof and Prandtl numbers demonstrate the relationship to the temperature distributions. The effects of the magnetic field and the non-Newtonian parameters were also illustrated, as these parameters influence the velocity distribution of the fluid flow.

In this paper, a new numerical method which is based on the coupling between multiscale method and meshless method with penalty is developed for 2D Burgers’ equation. The advantage of meshless method over the finite element method (FEM) is that remeshing process is not required. This is because the meshless method approximation is constructed entirely in terms of a set of nodes. Since the moving least squares (MLS) shape function does not satisfy the Kronecker delta property, so penalty method is adopted to enforce the essential boundary conditions in this paper. In order to obtain the fine scale approximation, the local enrichment basis is applied. The local enrichment basis may adopt the polynomial basis functions or any other analytical basis functions. Here, the polynomial basis functions are chosen as local enrichment basis. This multiscale meshless method with penalty will provide a more accurate result especially in the critical region which requires higher accuracy. It is believed that this proposed method is an attractive approach for solving more general problems which involve large deformation.