Related papers: An asynchronous leapfrog method II
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…
This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…
Algorithmic regularization uses a transformation of the equations of motion such that the leapfrog algorithm produces exact trajectories for two-body motion as well as regular results in numerical integration of the motion of strongly…
We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the…
Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's derivative. The time mesh is refined near the initial time to…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors. The new schemes stagger field variables in both time and…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…
A review of the most popular Linear Multistep (LM) Methods for solving Ordinary Differential Equations numerically is presented. These methods are first derived from first principles, and are discussed in terms of their order, consistency,…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e. numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is…
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…
A class of explicit pseudo two-step Runge-Kutta-Nystr\"{o}m (GEPTRKN) methods for solving second-order initial value problems $y'' = f(t,y,y')$, $y(t_0) = y_0$, $y'(t_0)=y'_0$ has been studied. This new class of methods can be considered a…
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…