We apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems increases linearly with the number of stages of the underlying Runge-Kutta method, resulting in high linear alg...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

Sugiura, H. and T. Torii, A method for constructing generalized Runge-Kutta methods, Journal of Computational and Applied Mathematics 38 (1991) 399-410. In the implementation of an implicit Runge-Kutta formula, we need to solve systems of nonlinear equations. In this paper, we analyze the Newton iteration process and a modified Newton iteration process for solving these equations. Then we propo...

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties, which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local tr...

In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally ...

Building military simulations requires bridging the gap between the knowledge of commanders and computer representations of that knowledge. A significant part of this knowledge concerns military tasks, their interactions, and an understanding of how to grade their achievement. Action Models describe the complex spacial and temporal dynamics of goal directed tasks with a graphical notation. Comm...

Based on M-estimate, the problem of robust estimation fusion in decentralized architecture when the sensor noises are contaminated by outliers is considered. A simple robust Kalman filtering (RKF) scheme with weighted matrices of innovation sequences is introduced for local state estimation. Then, to avoid both the inconsistency of the Kalman filter and the performance conservation of the covar...