In this paper, we consider non-linear Ginsburg-Pitaevski-Gross equation with the Rosen-Morse and modifiedWoods-Saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. We use the Runge- Kutta-Fehlberg approximation method to solve the resulting non-linear equation.    

Based on the homotopy analysis method (HAM), an efficient approach is proposed for obtaining approximate series solutions to fourth order two-point boundary value problems. We apply the approach to a linear problem which involves a parameter c and cannot be solved by other analytical methods for large values of c, and obtain convergent series solutions which agree very well with the exact solut...

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Gene...

Generalized Runge-Kutta Processes for stiff systems of ordinary differential equations usually require an accurate evaluation of a Jacobian at every step. However, it is possible to derive processes which are Internally S-stable when an accurate Jacobian is used but still remain consistent and highly stable if an approximate Jacobian is used. It is shown that these processes require at least as...

The present paper deals with the study of fluid flow and heat transfer characteristics occurring during the melting process due to a stretching surface in micropolar fluid with thermal radiation. A uniform magnetic field is applied normal to surface. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformati...

In this paper, we investigate the combined effects of buoyancy force and Navier slip on the entropy generation rate in a vertical porous channel with wall suction/injection. The nonlinear model problem is tackled numerically using Runge–Kutta–Fehlberg method with shooting technique. Both the velocity and temperature profiles are obtained and utilized to compute the entropy generation number. Th...

This paper provides a nice example to illustrate that without supporting analysis, a numerical simulation may lead to incorrect conclusions. We explore a pedagogical example of failure of Runge–Kutta–Felberg (RKF) algorithms for a simple dynamical system that models the coupling of two oscillators. Although the system appears to be well-behaved, the explicit RKF solvers provide erratic numerica...

The present work investigates numerically the inherent irreversibility in a steady flow of a couple stress fluid through a vertical channel packed with saturated porous substances. The First and Second Laws of Thermodynamics are applied to analyze the problem. The nonlinear governing equations in Cartesian coordinates are obtained and solved numerically using shooting methods together with a Ru...

Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD) convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field of uniform strength is presented. The Rosseland model for the conduction radiat...

This paper focuses on the formal modeling, simulation, and analysis of interacting hybrid systems that influence each other’s continuous behaviors. We define in the rewriting-logic-based Real-Time Maude tool a method for the numerical approximation of the continuous dynamics specified by ordinary differential equations. We adapt the Runge-Kutta-Fehlberg 4/5 method to define an adaptive-step-siz...