In this work we introduce a new approach to Dynamical Monte Carlo methods to simulate markovian processes. We apply this approach to formulate and study an epidemic generalized SIRS model. The results are in excellent agreement with the fourth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is no longer applicable...

We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit ...

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the max...

Time-stepping methods that guarantee to avoid spurious fixed points are said to be regular. For fixed stepsize Runge-Kutta formulas, this concept has been well studied. Here, the theory of regularity is extended to the case of embedded Runge-Kutta pairs used in variable stepsize mode with local error control. First, the limiting case of a zero error tolerance is considered. A recursive regulari...

Abstract— General linear methods (GLM) apply to a large family of numerical methods for ordinary differential equations, with RungeKutta (RK) and Almost Runge-Kutta (ARK) methods as two out of a number of special cases. In this paper, we have investigated the efficacy of Richardson extrapolation (RE) technique as a means of obtaining viable and acceptable estimates of the local truncation error...

In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge–Kutta method, which is called the fractional step Runge–Kutta met...

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...

In this paper, an interpolation method for solving linear diierential equations was developed using multiquadric scheme. Unlike most iterative formula , this method provides a global interpolation formulae for the solution. Numerical examples show that this method ooers a higher degree of accuracy than Runge-Kutta formula and the iterative multistep methods developed by Hyman (1978).

We present a full implementation of the parareal algorithm—an integration technique to solve di erential equations in parallel— in the Julia programming language for a fully general, rst-order, initial-value problem. Our implementation accepts both coarse and ne integrators as functional arguments. We use Euler’s method and another Runge-Kutta integration technique as the integrators in our exp...

This paper presents a new simple technique to improve the order behaviour of Runge-Kutta methods when applied to index 2 DAEs. It is then shown how this can be incorporated into a more eecient version of the code RADAU5 developed by E. Hairer and G. Wanner.