a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

We introduce a novel computational framework for the multiscale simulation of higher-order continua that allows consideration first-, second-, and third-order effects at both micro- macro-level. In line with classical two-scale approaches, we describe microstructure via representative volume elements are attached each integration point macroscopic problem. To take account extended continuity re...

This paper presents the case for the use of higher-order logic as a foundation for computational logic. A suitable polymorphicallytyped, higher-order logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representation purposes is presented. The approach to representing individuals is illustrated with some examp...

INTRODUCTION The paper presents a new multiscale framework that is both mathematically rigorous and practical in the sense that it has been successfully applied in aerospace, automotive and civil engineering industries. The “rigor” aspect of the method is provided by recently developed computational continua (C) formulation (Fish and Kuznetsov, 2009), which is endowed with fine-scale details, i...

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