Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-steppingmethod to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods ...

Economic and econometric analysis of continuous-time affine asset pricing models often necessitates solving systems of ordinary differential equations (ODEs) numerically. Explicit Runge-Kutta methods have been suggested to solve these ODEs in both the theoretical finance and financial econometrics literature. In this paper we show that under many empirically relevant circumstances the ODEs invo...

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide si...

Shale, like many other sedimentary rocks, is typically heterogeneous and anisotropic and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based on the lattice discrete particle model is formulated to capture these features. Material anisotropy is introduced through an approximated geometric descrip...

The Immersed Boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability con...

An efficient, non-stiff boundary integral method for the initial value problem for interfacial Darcy flow (which is a model of porous media flow) in three space dimensions is presented. We consider a ‘doubly-periodic’ interface separating two fluids, with surface tension present at the boundary. Surface tension introduces high order (i.e., high derivative) terms in the governing equation, and t...

In the present paper effect of angle of attack on stability derivatives in pitch of delta wing for the attached shock case is been studied. A strip theory is used in which strips at different span-wise locations are independent. This combines with the similitude to give a piston theory. In the present theory, the similitude, and the piston theory have been extended to a flat wing with straight ...

Stabilized Runge–Kutta methods are especially efficient for the numerical solution of large systems stiff nonlinear differential equations because they fully explicit. For semi-discrete parabolic problems, instance, stabilized overcome stringent stability condition standard without sacrificing explicitness. However, when stiffness is only induced by a few components, as in presence spatially lo...

We consider a class of ordinary differential equations mixing slow and fast variations with varying stiffness (from non-stiff to strongly dissipative). Such models appear for instance in population dynamics or propagation phenomena. develop multi-scale approach by splitting the into micro part macro part, from which original has been removed. then show that both parts can be simulated numerical...

the track stiffness experienced by a train will vary along the track. sometimes the stiffness variation may be very large within a short distance. one example is when an unsupported sleeper is hanging in the rail. track stiffness is then, locally at that sleeper, very low. at insulated joints the bending stiffness of the rail has a discontinuity implying a discontinuity also of the track stiffn...