We presented the numerical technique to approximately solve the pulse propagation equation. Two efficient methods for this problem, the Split-Step Fourier and the fourth order Runge-Kutta methods are considered. Their high accuracy are shown by comparison with analytical solutions in some particular situations. Our numerical experiments are implemented for soliton propagation and interacting hi...

In this study we develop high order numerical methods to capture the spatiotemporal dynamics of a generalized Kolmogorov-Petrovskii-Piskunov (KPP) equation characterized by density dependent non-linear diffusion. Towards this direction we consider third order Strong Stability Preserving Runge-Kutta (SSPRK) temporal discretization schemes coupled with the fourth order Hermite cubic Collocation (...

The orbital dynamics of an artificial satellite in the Earth’s atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange’s planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrat...

The entropy generation during hydromagnetic boundary layer flow of a viscous incompressible electrically conducting fluid due to radial stretching sheet with Newtonian heating in the presence of a transverse magnetic field and the thermal radiation has been analyzed. The governing equations are then solved numerically by using the fourth order Runge-Kutta method with shooting technique. The eff...

The attitude algorithms can enormously affect the navigation accuracy of SINS and Runge-kutta algorithm, Peano-Baker approximation algorithm rotation vector are common in engineering application. Analysis comparison done to above three this paper, simulated verified under coning motion result show that condition low angle vibration , fourth-order has best comprehensiveperformance.

We develop a two-dimensional solver for the acoustic wave equation with spatially varying coefficients. In what is a new approach, we use a basis of approximate prolate spheroidal wavefunctions and construct derivative operators that incorporate boundary and interface conditions. Writing the wave equation as a first-order system, we evolve the equation in time using the matrix exponential. Comp...

The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting multi-derivative extension of midpoint method we have obtained a new implicit four, for numerical solution first-order differential equations. is symplectic and suitable both initial boundary value Hamiltonian pro...

This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) timemarching methods to the generalized summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods are shown to retain: A and L-stability, as well as superconvergence of integral functionals when integrated with the quadrature associated with the discretization. This also implies that...