Exponential Runge-Kutta (ERK) and partitioned exponential Runge-Kutta (PERK) 4 methods are developed for solving initial value problems with vector fields that can be split into con5 servative and linear non-conservative parts. The focus is on linearly damped ordinary differential 6 equations, that possess certain invariants when the damping coefficient is zero, but, in the presence of 7 consta...

in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...

A high-order accurate method for the numerical solution of the incompressible Navier-Stokes equations is developed. Fourth–order, explicit, finite difference schemes on staggered grids are used for space discretization. The explicit, fourth–order Runge–Kutta method is used for time marching. Incompressibility is enforce for each Runge–Kutta stage either by a local pressure correction, which is ...

A modified Boris-like integration, in which the spatial coordinate is the independent variable, is derived. This spatial-Boris integration method is useful for beam simulations, in which the independent variable is often the distance along the beam. The new integration method is second order accurate, requires only one force calculation per particle per step, and preserves conserved quantities ...