An optimization method based on the Legendre wavelets for 3D rotating,squeezing and stretching magnetohydrodymanic flow in a channel with porous wall

In this paper, the 3D flow in a rotating channel with the lower permeable stretching wall is investigated. The unsteady squeezing flow in the presence of transverse magnetic flux is mathematically modeled by utilizing Navier-Stokes equations. A new optimal wavelet method based on coupling the Legendre wavelets and the hat functions with some auxiliary convergence-control parameters is proposed to solve the obtained fourth-order system of nonlinear differential equations. In the proposed method, the residual function and its error of norm two are employed for converting the main problem into an optimization one to optimally choose the auxiliary convergence-control parameters. The main idea behind this approach is to reduce solving such problems to those of solving optimization ones which greatly simplifies the problem and also leads to obtaining a good approximate solution for the problem under consideration.