We construct the cell-centered Finite Volume discretization of the twodimensional inviscid primitive equations in a domain with topography. To compute the numerical fluxes, the so-called Upwind Scheme (US) and the Central-Upwind Scheme (CUS) are introduced. For the time discretization, we use the classical 4th order RungeKutta method. We verify, with our numerical simulations, that the US (or C...

An improved scheme has been developed to solve the standard propagation equations (SPE) for Erbium doped fiber sources (EDFS). The scheme uses Rosenbrock algorithm based on implicit differentiation methods. The profiles of Forward Amplified Spontaneous Emission (FASE), Backward Amplified Spontaneous Emission (BASE) and Pump power along the fiber are presented and compared with the results of co...

The purpose of this article is the comparison of a cylindrical ion trap supplied by a periodic impulsional potential with quadrupole ion trap. To compute the five stability regions for the cylindrical ion trap (CIT) and quadrupole ion trap (QIT) in the a − q plane we use the RungeKutta method with the fifth order derivative approximations. The first up to five stability regions obtained in this...

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...

The classical two-phase Stefan problem in level set formulation is considered. The implementation of a solver on triangular grids is described. Extended finite elements (X-FEM) in space and an implicit Euler method in time are used to approximate the temperature. For the level set equation, a discontinuous Galerkin (DG) and a strong stability preserving (SSP) RungeKutta scheme are employed. Pol...

In this paper we analyse the stability of weak discrete stationary shocks. The difference approximation is conservative, dissipative and k-th order accurate (k = 1 or k = 3). In Sections 1-3, following the previous results of D. Michelson we adapt the multistep methods RungeKutta and Adams-Bashforth to solve systems of conservation laws. In section 4 we analyse the stability of the numerical me...

In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods...

In this paper we analyze numerical optimization procedures in the context of level set based image segmentation. The Chan-Vese functional for image segmentation is a general and popular variational model. Given the corresponding Euler-Lagrange equation to the ChanVese functional the region based segmentation is usually done by solving a differential equation as an initial value problem. While m...

General second-order, variable-density, three-step and four-step projection methods are developed to simulate unsteady incompressible interfacial flows. A high-accuracy, variabledensity RKCN projection method is presented, in which the three-stage, low-storage RungeKutta technique and second-order semi-implicit Crank-Nicholson technique are employed to temporally update the convective and diffu...

Based on high order approximation of L-stable RungeKutta methods for the Riemann-Liouville fractional derivatives, several classes of high order fractional Runge-Kutta methods for solving nonlinear fractional differential equation are constructed. Consistency, convergence and stability analysis of the numerical methods are given. Numerical experiments show that the proposed methods are efficien...