Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed pneumonia. Computing techniques have significant role science, engineering, many other fields. In this study, we focused on efficiency numerical via computer programs. We s...

We study the problem of efficient integration of variational equations in multi-dimensional Hamiltonian systems. For this purpose, we consider a Runge-Kutta-type integrator, a Taylor series expansion method and the so-called ‘Tangent Map’ (TM) technique based on symplectic integration schemes, and apply them to the Fermi-Pasta-Ulam β (FPU-β) lattice of N nonlinearly coupled oscillators, with N ...

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...

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...

To analyze a harmonically Van der Pol oscillator, this work used combination of graphs, time steps distribution, adaptive Runge-Kutta, and fourth order algorithms. The goal is to examine the performance third Runge-Kutta algorithms in finding chaotic solutions for excited oscillator. Fourth-order favor larger are thus faster execute than third-order all circumstances studied. accuracy data acqu...

New software based on explicit Runge-Kutta formulas have been developed to replace well-established, widely-used codes written by the authors (RKF45 and its successors in the SLATEC Library and the NAG Fortran 77 Library Runge-Kutta codes). The new software has greater functionality than its predecessors. Also, it is more eecient, more robust and better documented.

This paper presents a family of Runge{Kutta type integration schemes of arbitrarily high order for diierential equations evolving on manifolds. We prove that any classical Runge{Kutta method can be turned into an invariant method of the same order on a general homogeneous manifold, and present a family of algorithms that are relatively simple to implement.