We prove that to every rational function R(z) satisfying R(−z)R(z) = 1, there exists a symplectic Runge-Kutta method with R(z) as stability function. Moreover, we give a surprising relation between the poles of R(z) and the weights of the quadrature formula associated with a symplectic Runge-Kutta method.

In this paper, Optimal Homotopy Asymptotic Method (OHAM) is combined with Galerkin method to investigate the MHD Jeffery-Hamel flows in non-parallel walls for strongly nonlinear ordinary differential equations. Results for velocity profiles in divergent and convergent channels for various values of Hartmann and Reynolds numbers are compared with numerical method (the Runge-Kutta method of order...

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear...

Analytical solutions for the problem of radiation of sound from a duct with flow have been shown to serve as an important first model for acoustic engine-aircraft engineering applications, useful for understanding the physics and for validating and benchmarking numerical solutions. The probably most important steps were taken by Levine & Schwinger and Munt. He showed that application of the Kut...

We are concerned with the solution of time-dependent nonlinear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge-Kutta-type time stepping (discretisation in time). The introduced nonlinear blending procedure allows us to retain the explicit character of the time stepping ...

In this article, we investigate the execution of a meshless method line (MMOL) to solve general seventh-order Korteweg-de Vries (KdV7) equations numerically. The suggested technique uses radial basis functions (RBF) for spatial derivatives and Runge-Kutta (RK) time governing equation. To produce an efficient numerical solution, three different types RBF are used. method?s output is successfully...

This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints ...

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple inter...

The effect of temperature-dependent viscosity on heat transfer over a continuous moving surface with variable internal heat generation in micropolar fluids is studied. The fluid viscosity is assumed to vary as inverse linear function of temperature. The governing equations are transformed into dimensionless forms using the stream function and suitable variables then solved numerically using the...

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...