17 papers · ranked by Valyu relevance
Ronald F. Boisvert, Michael J. Donahue, Daniel W. Lozier, Robert McMichael + 1 more
'Robert McMichael' 'Bert W. Rust'] In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of…
Chang F Quo, May D Wang
Background This article provides guidelines for selecting optimal numerical solvers for biomolecular system models. Because various parameters of the same system could have drastically different ranges from 10-15 to 1010, the ODEs can be stiff and ill-conditioned, resulting in non-unique, non-existing, or…
Nikolaos P. Bakas
In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or…
Cristian Pisarciuc, Ioan Dan, Romeo Cioară, Alessandro Pirondi
Finite element analysis of complex bodies is frequently used in design to determine the size of deformations. Successive iterations, with progressive refinement of mesh densities, are most often required to obtain a sufficiently accurate convergent numerical solution. This process is costly, time consuming, and…
Augusto Badke Neto, Webe João Mansur, Walnório Graça Ferreira
This work presents a new method, the SOR_FEM, spurious oscillation reduction-FEM, that uses analytical solutions of simple problems to find numerical solutions of more complex problems to reduce the spurious oscillations that occur due to solution discontinuity. With the proposed method it is possible to find numerical…
P. K. Pandey
In this article, we present a novel second order numerical method for solving third order boundary value problems using the quartic polynomial splines. We establish the convergence of the method. We present numerical experiments to demonstrate the efficiency of the method and validity of our second order method, which…
Vagelis Plevris, Afaq Ahmad
This study extends the use of symbolic computation in matrix structural analysis to plane trusses, expanding on previous work that focused on continuous beams. We present a fully open-source MATLAB program, available on GitHub, that performs symbolic analysis of 2D trusses subjected to point loads, applicable to any…
Wojciech Wawrzynski
Each Duffing equation has an unstable solution area with a boundary, which is also a line of bifurcation. Generally, in a system that can be modeled by the Duffing equation, bifurcations can occur at frequencies lower than the origin point frequency of the unstable solution area for a softening system and at higher…
Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Muhammad Usman Ashraf + 1 more
'Muhammad Usman Ashraf' 'Mehvish Naz'] This article suggests a fourth-order numerical approach for solving ordinary differential equations (ODEs) that are both linear and nonlinear. The suggested scheme is an explicit predictor-corrector scheme. For linear ODE, the proposed numerical scheme's stability area is…
Shahanaz Parvin, Siti Suzilliana Putri Mohamed Isa, Fuad S. Al- Duais, Syed M. Hussain + 4 more
'Syed M. Hussain' 'Wasim Jamshed' 'Rabia Safdar' 'Mohamed R. Eid' 'Oluwole Daniel Makinde'] A mathematical model of 2D-double diffusive layer flow model of boundary in MHD Maxwell fluid created by a sloping slope surface is constructed in this paper. The numerical findings of non-Newtonian fluid are important to the…
Ibtehal Alazman, Badr Saad Thaar Alkahtani, Manvendra Narayan Mishra
In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in $1+1$-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such…
Jinxing Liu, Muhammad Nadeem, M. S. Osman, Yahya Alsayaad
Many scientific phenomena are linked to wave problems. This paper presents an effective and suitable technique for generating approximation solutions to multi-dimensional problems associated with wave propagation. We adopt a new iterative strategy to reduce the numerical work with minimum time efficiency compared to…
Liru Mu, Xinlong Feng, José F. F. Mendes
In this paper, the radial basis function finite difference method is used to solve two-dimensional steady incompressible Navier-Stokes equations. First, the radial basis function finite difference method with polynomial is used to discretize the spatial operator. Then, the Oseen iterative scheme is used to deal with…
Tomas Houba, Arnob Dasgupta, Shivasubramanian Gopalakrishnan, Ryan Gosse + 1 more
'Ryan Gosse' 'Subrata Roy'] The scalability and efficiency of numerical methods on parallel computer architectures is of prime importance as we march towards exascale computing. Classical methods like finite difference schemes and finite volume methods have inherent roadblocks in their mathematical construction to…
Majeed A. Yousif, Faraidun K. Hamasalh, Ahmad Zeeshan, Mohamed Abdelwahed + 1 more
'Mohamed Abdelwahed' 'Muhammad Mubashir Bhatti'] This research presents a novel conformable-Caputo fractional non-polynomial spline method for solving the time-fractional Korteweg-de Vries (KdV) equation. Emphasizing numerical analysis and algorithm development, the method offers enhanced precision and modeling…
Jaroslav Rojíček, Jakub Cienciala, Martin Fusek
This article explores the structural identifiability of parameters within non-linear physical models, focussing specifically on the Anand material model. The proposed procedure is structured in two key steps: first, a local analysis identifies the most suitable parameters for testing. Subsequently, these selected…
Karine Chemla
Ancient sources attest to the introduction of two families of numeration systems using place-value notations. In such systems, the base and its powers are always represented using position. The existence of a base of this kind is reflected by the repetitive character of the algorithms drawing on the place-value…