<p style='text-indent:20px;'>Classical symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation where all the terms in discrete Lagrangian are treated with same quadrature formula. We construct family of allowing use different formulas (primary and secondary) for Lagrangian. In particular, we study using Lobatto (with corresponding IIIA-B pair) as primary ...

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 paper continues earlier work by the same author concerning the stability and B-convergence properties of multistep Runge-Kutta methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. A series of sufficient conditions and necessary conditions for a multistep Runge-Kutta method to be algebraically stable, diagonally stable, Bor optimally B-convergent ...

In this paper we study numerical methods for Hybrid Fuzzy Differential equations by an appllication of the Runge-kutta Fehlberg method for fuzyy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

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...

This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of dusty fluid over an inclined stretching sheet with non-uniform heat source/sink, where the flow is generated due to a linear stretching of the sheet. Using a similarity transformation, the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential e...

Dynamic analysis of symmetric rotor with gyroscopic effect is performed in this study. First, equations of motion have been derived using Lagrange equation and then solved analytically by Homotopy Perturbation Method (HPM) and numerically appling Runge-Kutta-Fehlberg 4th-5th order method. Results are presented through graphs and table. Comparison of analytic outcomes with numerical ones showed ...

Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...