A numerical study of several time integration methods for solving the threedimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storag...

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time inte...

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We introduce a variational principle for field theories, referred to as the HamiltonPontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then d...

A MULTI-STEP IMPLICIT ITERATIVE PROCESS FOR COMMON FIXED POINTS OF GENERALIZED C-OPERATORS IN CONVEX METRIC SPACES Zahid Akhtar, Hafiz Fukhar-ud-din, Ali Ahmad and Muhammad Ibrahim 1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan. College of computer Science and information systems, Jazan University, Jazan, Saudi Arabia. Center for Advanced Studies ...

Recently, multi-time stepping methods have become very popular among scientist due to their high stability in problems with critical conditions. One important shortcoming of these methods backs to their high amount of uncontrolled amplitude decay. This study proposes a new multi-time stepping method in which the time step is split into two sub-steps. The first sub-step is solved using the well-...

A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems ...

The implicit Euler scheme of time variable and discrete exterior calculus can be united to find an unconditional stable approach, which is called implicit discrete exterior calculus. This technique for solving Maxwell’s equations in time domain is discussed, which provides flexibility in numerical computing on manifold. For some problems, it takes much less computational time to use the implici...

We describe and evaluate various implicit and semiimplicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of impli...