Related papers: Status of the differential transformation method

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…

In this study,a new method was presented by developing Reduced differential transform method in order to find approximate solution of partial differential equations. Here, RDTM with fixed grid size algorithm was developed for the first time…

High-order methods for convex and nonconvex optimization, particularly $p$th-order Adaptive Regularization Methods (AR$p$), have attracted significant research interest by naturally incorporating high-order Taylor models into adaptive…

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…

The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…

For academics and practitioners concerned with computers, business and mathematics, one central issue is supporting decision makers. In this paper, we propose a generalization of Decision Matrix Method (DMM), using Neutrosophic logic. It…

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately,…

In this paper we introduce the DMR -- a prototype-based method and network architecture for deep learning which is using a decision tree (DT)-based inference and synthetic data to balance the classes. It builds upon the recently introduced…

In this work, we spotted the light on one of the really important concepts and turned it into a mathematical branch instead of separate equations studied individually in different specializations of science. The existence and uniqueness of…

Differentially private (DP) tabular data synthesis generates artificial data that preserves the statistical properties of private data while safeguarding individual privacy. The emergence of diverse algorithms in recent years has introduced…

The recent theory of plausible and paradoxical reasoning (DSmT for short, or Dezert-Smarandache Theory), developed by the authors, appears to be a nice promising theoretical tools to solve many information fusion problems (for example in…

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…

The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…

Differential privacy (DP) has become the de facto standard of privacy preservation due to its strong protection and sound mathematical foundation, which is widely adopted in different applications such as big data analysis, graph data…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference…

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…

Digital memcomputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an…

Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly…

The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…