The existing tau-selection strategy, which was designed for explicit tau-leaping, is here modified to apply to implicit tau-leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency. Numerical testing demo...

The existing tau-selection strategy, which was designed for explicit tau leaping, is here modified to apply to implicit tau leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency is proposed. Numerical testing demo...

This article considers the influence of incompressibility on compliance and stiffness constants that appear in weakly nonlinear theory elasticity. The formulation first constraint applied to compliances, which gives explicit finite limits for second-, third-, fourth-order constants. stiffness/compliance relationships each order are derived used determine incompressible behavior Unlike compressi...

In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite element analysis. Bounds are derived for the eigenvalues and the condition numbers, which are valid for stiffness matrices based on a set of general basis functions that can be used in the p-version. For a set of hierarchi...

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semiimplicit schemes to remove this stiffness from the Immer...

Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses explicit stabilized Runge–Kutta methods, also known as Chebyshev methods. Implicit methods are great for very stiff problems of not very large dimension, while stabilized explicit methods are efficient for very big systems of not very large ...

BACKGROUND When humans are faced with an unstable task, two different stabilization mechanisms are possible: a high-stiffness strategy, based on the inherent elastic properties of muscles/tools/manipulated objects, or a low-stiffness strategy, based on an explicit positional feedback mechanism. Specific constraints related to the dynamics of the task and/or the neuromuscular system often force ...

A new technique for computation structural instability points using the finite element method is presented. The approach is based on the estimation of critical displacement pattern by writing an approximation of the tangent stiffness singularity condition at the instability point. The critical load is subsequently computed by using a secant load-displacement relationship. Details of this proced...