22 papers · ranked by Valyu relevance
Shovan Sourav Datta Pranta, Md Shafiqul Islam
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results using the Galerkin weighted residual approach with Bernstein polynomials. The…
Meena Joshi, Anita Tomar, Mohammad Sajid, S.K. Padaliya
In the present study, a novel version of the contraction theory on a relational partial metric space associated with a binary relation is exhibited. In this process, we observe that numerous relations can be used in many well-known fixed point theorems earlier introduced by multiple authors. We solve an elliptic…
Rusdrael Antony de Araújo Freire, Francisco Márcio Barboza, Marcelo Barboza
Numerical Approach Authors: ['Rusdrael Antony de Araújo Freire' 'Francisco Márcio Barboza' 'Marcelo Barboza'] This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in…
Yuanheng Wang, Barrira Jurrat, Muddasir Ejaz, Muhammad Azeem + 2 more
'M. I. Elashiry' 'Rehana Naz'] In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer’s fixed point…
Salima Kouser, Shafiq Ur Rehman, Yasser Elmasry, Waqar Azeem Khan + 3 more
'Fayyaz Ahmad' 'Hamza Khan' 'B. Omkar Lakshmi Jagan'] The Newton method is a classical method for solving systems of nonlinear equations and offers quadratic convergence. The order of convergence of the Newton method is optimal as it requires one evaluation for the system of nonlinear equations and the second for the…
Azhar Iqbal Kashif Butt, Nehad Ali Shah, Waheed Ahmad, Thongchai Botmart + 1 more
'Thongchai Botmart' 'Naeed Ahmad'] In this paper, we consider an isothermal glass tube drawing model consisting of three coupled nonlinear partial differential equations. The steady-state solution of this model is required in order to investigate its stability. With the given initial and boundary conditions, it is not…
Evgenii S. Baranovskii, Hang Xu, Jifeng Cui
In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is…
Volodymyr Denysiuk, Lyudmila Rybachuk
Many problems in science and technology often involve solving linear differential equations. Despite the well-developed theoretical methods for solving such equations, finding their exact solutions is difficult and often impossible. In such cases, the problem of finding approximate solutions to such equations is…
Davron Aslonqulovich Juraev, Ali Shokri, Daniela Marian, Renaldas Urniezius
'Renaldas Urniezius'] In this paper, on the basis of the Carleman matrix, we explicitly construct a regularized solution of the Cauchy problem for the matrix factorization of Helmholtz’s equation in an unbounded two-dimensional domain. The focus of this paper is on regularization formulas for solutions to the Cauchy…
Evgenii S. Baranovskii, Mikhail A. Artemov, Andrew N. Hrymak
In this paper, we consider a mathematical model for the flow of a dilute aqueous polymer solution through a heterogeneous porous medium. On the boundary of the flow region, the impermeability condition and a nonlinear Navier-type slip condition are prescribed. Our goal is to investigate the existence of weak solutions…
Jinye Shen, Heng Dai, Weizhang Huang
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state solution is taken as the solution of the underlying Bernoulli free boundary…
Muhammad Amjad, Haider Ali
Differential equations have void applications in several practical situations, sciences, and non-sciences as Euler–Lagrange equation in classical mechanics, Radioactive decay in nuclear physics, Navier– Stokes equations in fluid dynamics, Verhulst equation in biological population growth, Hodgkin– Huxley model in…
Adriana C. Briozzo
equation with Neumann condition Authors: ['Adriana C. Briozzo'] We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face x = 0, which is variable in time and a like Stefan convective condition on the free boundary. Through…
Anna Kovalenko, Natalia Chubyr, Aminat Uzdenova, Makhamet Urtenov + 1 more
'Weifeng Li'] At present, it is customary to consider the overlimit operating modes of electromembrane systems to be effective, and electroconvection as the main mechanism of overlimiting transfer. The breakdown of the space charge is a negative, “destructive” phenomenon, since after the breakdown the size and number…
David Thompson, Johan Gielis
Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Changin Oh, Kathleen P. Wilkie
We present the Toroidal Search Algorithm (TSA), a novel population-based metaheuristic optimization method inspired by the topology of a torus. Conventional metaheuristics frequently suffer from boundary stagnation, a phenomenon that severely degrades performance in bounded and high-dimensional search spaces. TSA…
Justin C. Bui, Éowyn Lucas, Eric W. Lees, Andrew K. Liu + 4 more
Carbon dioxide (CO2) must be removed from the atmosphere to mitigate the negative effects of climate change. However, the most scalable methods for removing CO2 from the air require heat from fossil-fuel combustion to produce pure CO2 and continuously regenerate the sorbent. Bipolar-membrane electrodialysis (BPM-ED) is…
Gerald S. Manning
An energy barrier model for a membrane yields new biophysical results. Here we explore both the equilibrium and time-dependent Nernst potential, capacitance and resistance, the resting potential, and osmosis.
István Kolossváry, Woody Sherman
Conformational sampling of complex biomolecules is an emerging frontier in drug discovery. Indeed, advances in lab-based structural biology and related computational approaches like AlphaFold have made great strides in obtaining static protein structures. However, biology is in constant motion and many important…
Rudra Prakash, Shaunak Sen
The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To…