Two new implicit–explicit, additive Runge–Kutta (ARK 2) methods are given with fourth-and
fifth-order formal accuracies, respectively. Both combine explicit Runge–Kutta (ERK) …

This article aims to understand the motion of the charged particles trapped in the Earth's
inner magnetosphere. The emphasis is on identifying the numerical scheme, which is …

The microelectronics area constantly demands better and improved circuit simulation tools.
Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials …

In this paper, a Semi-Lagrangian Runge-Kutta method is proposed to compute the
numerical solution of time-dependent partial differential equations. The method is based on …

This paper proposes new direct and acceleration numerical methods for solving Fractional
order Differential Equations (FDEs). For the Caputo differential operator with fractional order …

In this article, one-step semi-Lagrangian method is investigated for computing the numerical
solutions of the first-order time-dependent nonlinear partial differential equations in 1D with …