Two-step deferred correction algorithm for the problem of fluid film squeezed between rotating disks

Abstract

In this paper, a new collocation method is analyzed for the solution of a system of nonlinear differential equations arisen from modeling the flow of a Newtonian magnetic lubricant film with magnetic induction effects, squeezed between two rotating disks with a time-dependent distance. The source problem is a system of nonlinear partial differential equations which is converted to the system of fourth-order ordinary differential equations by some appropriate transformations. The problem is then transformed to an equivalent second-order system subject to its proper boundary conditions. Eighth-order superconvergent approximations are obtained for the solution based on sextic B-spline. High-order perturbations of the problem are used to find higher orders of convergence. We proceed the superconvergence in two successive steps by perturbing the right-hand side of the problem appropriately. The convergence of the method is analyzed via Green’s function approach. The numerical results verify the theoretical orders of convergence and show the efficiency of the methods as well.