This paper studies the effects of Natural convection and Thermal radiation on nanofluid over a non-linearly stretching sheet. The governing equation nonlinear partial differential equations flow is transformed to ordinary by using similarity transformation, earlier than being solved numerically through Rung-Kutta-Fehlberg method with shooting technique. numerical results have been obtained for ...

New software based on explicit Runge-Kutta formulas have been developed to replace well-established, widely-used codes written by the authors (RKF45 and its successors in the SLATEC Library and the NAG Fortran 77 Library Runge-Kutta codes). The new software has greater functionality than its predecessors. Also, it is more eecient, more robust and better documented.

A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently re...

Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that ...

The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size of the truncation error are considered. The optimum method is practically independent of the measure being used. Moreover, among methods of the same order which one might consider using the difference in size of the estimated error is not more than a factor of 2 or 3...

Analytical gas-permeation models for predicting the separation process across  membranes (exit compositions and area requirement) constitutes an important and necessary step in understanding the overall performance of  membrane modules. But, the exact (numerical) solution methods suffer from the complexity of the solution. Therefore, solutions of nonlinear ordinary differential equations th...

We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with sl...