In many applications, large systems of ordinary di erential equations (ODEs) have to be solved numerically that have both sti and nonsti parts. A popular approach in such cases is to integrate the sti parts implicitly and the nonsti parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linea...

The United Nations (2012) stated in a recent report that “as a middle-income country with strong growth, Thailand is determined to “leap frog” in development status. The ultimate goal is its transformation into a “developed, first-world nation, capable of sustaining long-term quality growth and lasting prosperity”. To this end, the Royal Thai Government has been resolute in seeking to consolida...

−A 300MHz CMOS seventh−order linear phase gm−C filter based on a current−mode multiple loop feedback (MLF) leap−frog (LF) structure is realized. The filter is implemented using a fully−differential linear operational transconductance amplifier (OTA) based on a source degeneration topology. PSpice simulations using a standard TSMC 0.18μm CMOS process with 2.5V power supply have shown that the cu...

1D-3V PIC Simulations (XPDP1) XPDP1, a 1D-3V PIC-MCC code (Verboncoeur et al., 1993), was used to simulate current-driven DC discharges. • leap-frog integration used for particle motion (2nd order accurate) • linear weighting of particles and fields used • 2nd-order finite difference solution of Poisson’s equation with 2nd-order center difference and boundary conditions to obtain the electric f...

Abstract. A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretisation and thus do not have a step size restricti...

A series of molecular dynamics (MD) simulations of nonlinear molecules has been performed to test the efficiency of newly introduced semianalytical second-order symplectic time-reversible MD integrators that combine MD and the standard theory of molecular vibrations. The simulation results indicate that for the same level of accuracy, the new algorithms allow significantly longer integration ti...

Optimal a priori error bounds are theoretically derived, and numerically verified, for approximate solutions to the 2D homogeneous wave equation obtained by spectral element method. To be precise, method studied here takes advantage of Gauss-Lobatto-Legendre quadrature, thus resulting in under-integrated elements but diagonal mass matrix. The approximation H1 is shown order O(hp) with respect s...

Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The is under various names (”Verlet, leap-frog,..”) most used in simulations of complex system Physics and Chemistry, it also applied Astrophysics. His discrete dynamics has same qualities as exact analytic for continuous space time with reversibility, symplecticity conse...