In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using RungeKutta convolution quadrature in time and a Galerkin method in space. We analyze the involved operators in the Laplace domain and obtain convergence results for the fully discrete scheme. Numerical experiments indicate the...

We consider the adaptive strategies applicable to a simple model describing the phase lock of two coupled oscillators. This model has been used to show an instance of failure of the ODE45 RungeKutta-Felberg solver implemented within the MATLAB ODE suite, see [J. D. Skufca. Analysis still matters: a surprising instance of failure of Runge-KuttaFelberg ODE solvers. SIAM Review, 46:729-737, 2004]....

The point-source traveltime field has an upwind singularity at the source point. Consequently, all formally high-order, finite-difference eikonal solvers exhibit firstorder convergence and relatively large errors. Adaptive upwind finite-difference methods based on high-order Weighted Essentially NonOscillatory (WENO) RungeKutta difference schemes for the paraxial eikonal equation overcome this ...

A numerical investigation has been done to study the impact of nonlinear magnetic field, nonlinear thermal radiation, variable thickness, Brownian motion on flow and heat transfer characteristics (i.e. skin friction and surface heat flux) as a physical application. Moreover, the impact of these forces on the rate of cooling and the mechanical properties (i.e. hardness, ductility...) of the surf...

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum mechanical models: a symmetric one V (x) = |x|/2; and an asymmetric one V (x) = ∞, for x < 0 and V (x) = x, for x ≥ 0. The results for the spectrum, wave functions...

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...

Analytical solution for hyperchaotic systems have attracted increasing interest in recent years. In this paper, numerical-analytical solution for hyperchaotic Rössler system is obtained via multistage homotopy analysis method (MSHAM). An analytical form of the solution within each time interval is given, which is not possible using standard numerical methods. The numerical results obtained by t...

In this paper we introduce a new method of spatio-temporal discretization for partial differential equations in variational form. This method generalizes the method of Marsden et al in that it uses a systematic approach to discrete jet spaces based on the finite element method. The resulting method is used to derive integrators for the Nonlinear Schrödinger (NLS) equation which exhibit superior...

A comprehensive study of thermal radiation on a steady two-dimensional laminar flow of a viscous incompressible electrically conducting micropolar fluid past a stretching surface embedded in a non-Darcian porous medium is analyzed numerically. The governing equations of momentum, angular momentum, and energy equations are solved numerically using RungeKutta fourth order method with shooting tec...

An error analysis is given for convolution quadratures based on strongly A-stable RungeKutta methods, for the non-sectorial case of a convolution kernel with a Laplace transform that is polynomially bounded in a half-plane. The order of approximation depends on the classical order and stage order of the Runge-Kutta method and on the growth exponent of the Laplace transform. Numerical experiment...