This paper focuses on a steady two-dimensional slip flow of a viscous incompressible electrically conducting and radiating fluid past a linearly stretching sheet with temperature dependent viscosity is taking into account. The governing boundary layer equations are solved by using Runge-Kutta fourth order technique along with shooting method. The influence of various governing parameters on the...

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-di usion equation. Spatial discretization is by the -scheme or the fourth order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for ow computations, and...

The effect of nanofluids on chaotic convection in a fluid layer heated from below was studied in this paper for low Prandtl number based on the theory of dynamical systems. A low-dimensional, Lorenz-like model was obtained using Galerkin-truncated approximations. The fourth-order Runge-Kuttamethodwas employed to solve the nonlinear system. The results show that inhibition of chaotic convection ...

A new implementation of boundary condition based on the half-covolume and bounce-back rule for the non-equilibrium distribution function for the finite volume LBM is proposed here. The numerical simulation results for the expansion channel flow and driven cavity problem indicate that this method is workable for arbitrary meshes. In addition, the fourth order Runge–Kutta scheme is found to be a ...

We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the...

This paper researches the accuracy of the Differential Transformation Method (DTM) for solving the Holling Tanner models which are described as two-dimensional system of ODES with quadratic and rational nonlinearities. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. The direct symboli...

A system of ordinary differential equations, which describes the interaction of HIV and T -cells in the immune system is utilized, and optimal controls representing drug treatment strategies of this model are explored. Two types of treatments are used, and existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically ...

-A pair of explicit Runge-Kutta formulas of orders 4 and 5 is derived. It is significantly more efficient than the Fehlberg and Dormand-Prince pairs, and by standard measures it is of at least as high quality. There are two independent estimates of the local error. The local error of the interpolant is, to leading order, a problem-independent function of the local error at the end of the step. ...

This part is concerned with the numerical solution of initial value problems for systems of ordinary differential equations. We will introduce the most basic one-step methods, beginning with the most basic Euler scheme, and working up to the extremely popular Runge–Kutta fourth order method that can be successfully employed in most situations. We end with a brief discussion of stiff differentia...