the aim of the present paper is to study the cu-water nanofluid flow and heat transfer characteristics of a stretching permeable cylinder. thermal radiation effect is considered in energy equation. the governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similari...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

2. General Remarks Second order ODEs are much harder to solve than first order ODEs. First of all, a second order linear ODE has two linearly independent solutions and a general solution is a linear combination of these two solutions. In addition, many popular second order ODEs have singular points. Except for a few cases, the solutions have no simple mathematical expression. However, there is ...

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-order with dispersive order six and 'small' principal local truncation error terms and dissipation constant. The analysis of phase-lag, dissipatio...

To integrate large systems of ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on embedded, explicit Runge-Kutta (RK) formulas. The order of accuracy of such methods depends on interpolating certain solution components with a polynomial of sufficiently high degree. By analyzing the method applied to a simple test eq...