In the current research with novel first and second differentiations of a yield function, Euler forward along with Euler backward with its consistent elastic-plastic modulus are newly implemented in finite element program in rate-independent plasticity. An elastic-plastic internally pressurized thick walled cylinder is analyzed with four famous criteria including both pressure dependent and ind...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

one of the new research fields in plasticity is related to choosing a proper non-associated flow rule (nafr), instead of the associated one (afr), to predict the experimental results more accurately. the idea of the current research is derived from combining von mises and tresca criteria in the places of yield and plastic potential surfaces in rate-independent plasticity.  this idea is implemen...

which is uniform with respect to λ > 0. Recall that we showed that this stability estimate is preserved by the implicit Euler method. However, the explicit Euler method is only stable provided that ∆t < 2/λ, so its stability is not uniform in λ. One consequence is that it is less efficient to compute with the explicit Euler method over long time intervals. Note that in this example, we also hav...

Abstract. In this paper, a linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids. Some new a priori bounds are obtained for the solution under realistically assumed conditions on the data. Further, the exponential decay properties for the exact as well as the discrete solutions are established. Finally, a priori error estim...

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(∆tγ) for any γ < 1 2 . We also prove that the scheme converges uniformly in the strong Lp-sense but wi...

Abstract. This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion coefficient functions such as the stochastic Ginzburg-Landau equation and the 3/2-volatility model from mathematical finance. Our analysis of the ...

When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the e...

Dynamical systems can often be decomposed into loosely coupled subsystems. The system of ordinary differential equations (ODEs) modelling such a problem can then be partitioned corresponding to the subsystems, and the loose couplings can be exploited by special integration methods to solve the problem using a parallel computer or just solve the problem more efficiently than by standard methods....

This paper is concerned with finding numerical solutions of a flow of ODE solutions. It describes a new method, based on Euler Backward method and interpolation, for finding solutions of autonomous problems. The special aspect is that this method is explicit, and resolves the flow with similar accuracy as Euler Backward method, even when the problem is stiff. An analysis is given of both stabil...