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...

In this report a model of Differential and Algebraic Equations (DAE) for the dynamics of a rotating laser deflecting system, which is a multibody system, is derived. Classical numerical integration software isn't however able to solve these equations, so the possiblity to transform the model into a set of Ordinary Differential Equations (ODE) is investigated. Elimination of the algebraic equati...

This paper addresses the issue of lemma generation in a k-induction-based formal analysis of transition systems, in the linear real/integer arithmetic fragment. A backward analysis, powered by quantifier elimination, is used to output preimages of the negation of the proof objective, viewed as unauthorized states, or gray states. Two heuristics are proposed to take advantage of this source of i...

If is the computed solution to a tridiagonal system Ax b obtained by Gaussian elimination, what is the "best" bound available for the error x and how can it be computed efficiently? This question is answered using backward error analysis, perturbation theory, and properties of the LU factorization of A. For three practically important classes of tridiagonal matrix, those that are symmetric posi...

We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore is capable of correctly predicting stability or instability of an algorithm. By means of nontrivial examples, such as the componentwise backward stability analys...

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...

In decision-theoretic planning, the problem of planning under uncertainty is formulated as a multidimensional, or factoredMDP. Traditional dynamic programming techniques are ine cient for solving factored MDPs whose state and action spaces are exponential in the number of the state and action variables, correspondingly. We focus on exploiting problems' structure imposed by variable independence...