24 papers · ranked by Valyu relevance
Yiannis Hadjimichael, David I. Ketcheson
The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal additive and perturbed monotonicitypreserving linear multistep methods are studied in the…
S. Ross Glandon, Mahesh Narayanamurthi, Adrian Sandu
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing restrictions on timestep size. However, implicit methods require solutions to one or more…
Onur Teymur, Konstantinos C. Zygalakis, Ben Calderhead
We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have…
Robert Plato
We study quadrature methods for solving Volterra integral equations of the first kind with smooth kernels under the presence of noise in the right-hand sides, with the quadrature methods being generated by linear multistep methods. The regularizing properties of an a priori choice of the step size are analyzed, with…
Samuel N Jator, Leong Lee
A Seventh-Order Linear Multistep Method (SOLMM) is developed and implemented in both predictor-corrector mode and block mode. The two approaches are compared by measuring their total number of function evaluations and CPU times. The stability property of the method is examined. This SOLMM is also compared with existing…
Ahmad Fadly Nurullah Rasedee, Mohammad Hasan Abdul Sathar, Khairil Iskandar Othman, Siti Raihana Hamzah + 2 more
'Khairil Iskandar Othman' 'Siti Raihana Hamzah' 'Norizarina Ishak' 'Naramgari Sandeep'] Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods…
Giuseppe Izzo, Eleonora Messina, Mario Pezzella, Antonia Vecchio
systems Authors: ['Giuseppe Izzo' 'Eleonora Messina' 'Mario Pezzella' 'Antonia Vecchio'] Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that…
Boris Faleichik
The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form of an explicit linear multistep method we suggest to adaptively choose its coefficients on each integration step in order to minimize the…
Wei Ming, Yukun Bao, Zhongyi Hu, Tao Xiong
The hybrid ARIMA-SVMs prediction models have been established recently, which take advantage of the unique strength of ARIMA and SVMs models in linear and nonlinear modeling, respectively. Built upon this hybrid ARIMA-SVMs models alike, this study goes further to extend them into the case of multistep-ahead prediction…
Mohammed S. Mechee, Mohammed Mahmood Salih
Background In this paper, we focus on deriving an efficient method for solving ordinary differential equations (ODEs) of sixth order, and then, we modify the proposed method for solving fractional differential equations (FDEs). Methods The methodology of this paper used the approach of derivation of implicit numerical…
Kai Rothauge, Eldad Haber, Uri M. Ascher
The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE system is solved using an exponential integrator. We also discuss the closely…
Khai Chien Lee, Muhammad Naeim Mohd Aris, Ishak Hashim, Norazak Senu
An efficient trigonometrical-fitted two-derivative multistep collocation (TF-TDMC) method using Legendre polynomials up to order five as the basis functions, has been developed for solving second-order ordinary differential equations with oscillatory solution effectively. Interpolation method of approximated power…
Nicholas A. Popp, Rachel L. Powell, Melinda K. Wheelock, Brendan D. Zapp + 11 more
Despite widespread advances in DNA sequencing, the functional consequences of most genetic variants remain poorly understood. Multiplexed Assays of Variant Effect (MAVEs) can measure the function of variants at scale, and are beginning to address this problem. However, MAVEs cannot readily be applied to the ∼10% of…
H.K. Al-Mahdawi, A. I Sidikova, Hussein Alkattan, Mostafa Abotaleb + 2 more
'Ammar Kadi' 'El-Sayed M El-kenawy'] We considered in this work the linear operator equation and used the Landweber iterative method as an iterative solver. After that, we used the multigrid method as an optimization method for obtaining an approximation solution with a highly accurate and fast process. A new parallel…
Yu Huo, Hongpei Li, Xiao Wang, Xiaochen Du + 1 more
When analysing two-dimensional data sets, scientists are often interested in regions where one variable depends linearly on the other. Typically they use an ad hoc method to do so. Here we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a data set into contiguous piece-wise…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Richard Border, Stephen Becker
Linear mixed-effects models (LMM) are a leading method in conducting genome-wide association studies (GWAS) but require residual maximum likelihood (REML) estimation of variance components, which is computationally demanding. Previous work has reduced the computational burden of variance component estimation by…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…
Marijn van Vliet, Riitta Salmelin
Linear machine learning models “learn” a data transformation by being exposed to examples of input with the desired output, forming the basis for a variety of powerful techniques for analyzing neuroimaging data. However, their ability to learn the desired transformation is limited by the quality and size of the example…
Daniel Kaschek, Wolfgang Mader, Mirjam Fehling-Kaschek, Marcus Rosenblatt + 1 more
In a wide variety of research elds, dynamic modeling is employed as an instrument to learn and understand complex systems. The differential equations involved in this process are usually non-linear and depend on many parameters whose values decide upon the characteristics of the emergent system. The inverse problem…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Carl Leake, Hunter Johnston, Lidia Smith, Daniele Mortari
Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural bending, and systems dynamics. While there are many other techniques for finding approximate solutions to these equations, this paper looks…
Authors not listed
Bonkowski and De Souza [Sol. Stat. Ionics 429, 116967 (2025)] provide a guide for performing molecular dynamics simulations of ion transport, including methods for estimating diffusion coefficients and their uncertainties from mean-squared displacement (MSD) data. The discussion of uncertainty in estimated diffusion…
Peng Zheng, Ryan Barber, Reed Sorensen, Christopher Murray + 1 more
Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and…