This paper is concerned with the numerical solution of implicit neutral functional diierential equations. Based on the continuous Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equations), two general one-step methods are formulated and their uniform order of approximation are discussed. Numerical stability of a class of Runge{Kutta-Collocatio...

Implicit Runge-Kutta methods are considered which combine the single-implicitness or diagonal-implicitness property with a zero first row in the coefficient matrix. Acceptable stability for stiff problems is retained by requiring the last stage of a step to be identical to the output value. This requirement, which corresponds to the FSAL property for explicit Runge-Kutta methods, allows the met...

To my beautiful wife, Ashley. For your unconditional love, faithful encouragement, and resolute support. You have always believed in and inspired the pursuit of my dreams. iv ACKNOWLEDGEMENTS I would first like to express my immense gratitude to my advisor, Dr. Glenn Sjoden. What started as an undergraduate summer research project transformed into my path in graduate school. As both an advisor ...

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed ...

This lecture is a survey of the theory of stability and error bounds for numerical methods for stii initial value problems. We begin with problems in singular perturbation form, where the distinction between \fast" and \slow" variables is clearest. Next we explain Kreiss's characterization of stii problems that includes singular perturbation problems as a special case. The requirement of unifor...

A new Runge-Kutta-Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince RungeKutta-Nyström method of algebraic order four[1]. Numerical illustrations indicate that the new method is much more efficient than the classical one.

the main purpose of this paper is to introduce a boundary layer analysis for the fluid flow andheat transfer characteristics of an incompressible nanofluid flowing over a permeable isothermalsurface moving continuously. the resulting system of non-linear ordinary differential equations issolved numerically using the fifth–order runge–kutta method with shooting techniques usingmatlab and maple s...

in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...

In this paper, we propose a functional fitting s-stage Runge-Kutta method which is based on the exact integration of the set of the linearly independent functions u i (t), (i = 1,. .. , s). The method is exact when the solution of the ODE can be expressed as the linear combination of u i (t), although the method has an error for general ODE. In this work we investigate the order of accuracy of ...

Abstract— The problem of Marangoni convection boundary layer flow in nanofluid with radiation effects is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Rung...