<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 ...

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 ...

Recently, global and local relaxation Runge–Kutta methods have been developed for guaranteeing the conservation, dissipation, or other solution properties general convex functionals whose dynamics are crucial an ordinary differential equation solution. These novel time integration procedures application in a wide range of problems that require dynamics-consistent stable numerical methods. The s...

In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both...

The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...

System theory for numerical analysis has recently become a focus of research. In this paper we regard dynamics of Newton’s method as a nonlinear feedback system and derive convergence conditions, based on the internal model principle and systems of Lur’e type. We then focus our attention on the analysis of the region of absolute stability of Runge-Kutta type methods. We derive a linear matrix i...