Related papers: Status of the differential transformation method
Waveform Relaxation method (WR) is a beautiful algorithm to solve Ordinary Differential Equations (ODEs). However, because of its poor convergence capability, it was rarely used. In this paper, we propose a new distributed algorithm, named…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
This paper presents an approach for the development of a number theoretic discrete Hilbert transform. The forward transformation has been applied by taking the odd reciprocals that occur in the DHT matrix with respect to a power of 2.…
A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of…
The Transfer Matrix Method (TMM) stands as the ubiquitous computational backbone for analyzing 1D wave propagation in layered media, underpinning critical product designs in photonics, seismology, and acoustics -- industries collectively…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the state given the dynamics (the forward problem), but here we…
Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…
In this paper, we interpret NDTM (NonDeterministic Turing Machine) used to define NP by tracing to the source of NP. Originally NP was defined as the class of problems solvable in polynomial time by a NDTM in the theorem of Cook, where the…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 2014, 112, 110401] can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy…
The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they…
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…