22 papers · ranked by Valyu relevance
В. Ж. Сакбаев, И. В. Волович
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the boundary values of the solution and its normal derivatives must satisfy. Linear…
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…
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…
Sandip Moi, Suvankar Biswas, Smita Pal(Sarkar)
In this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed.…
Mehmet Pakdemirli
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution…
Ahmed Salem Heilat, Nur Nadiah Abd Hamid, Ahmad Izani Md. Ismail
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, $\lambda _{1}$ and $\lambda _{2}$, play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error…
Riccardo Fazio
Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review Riccardo Fazio Department of Mathematics, Computer Science Physical Sciences and Earth Sciences, University of Messina Viale F. Stagno D'Alcontres, 31 98166 Messina, Italy E-mail: rfazio@unime.it Home-page…
Olexandr Polishchuk
—The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal…
Chengbo Zhai, Mengru Hao
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by −D0+ν1y1(t) = λ1a1(t)f(y1(t), y2(t)), − D0+ν2y2(t) = λ2a2(t)g(y1(t), y2(t)), where D0+ν is the standard Riemann-Liouville fractional derivative, ν1…
Ahmed Alsaedi, Sotiris K. Ntouyas, Bashir Ahmad
By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example.
Anthony N. Johnson, T.V. Hromadka II
The complex variable boundary element method (CVBEM) has been shown to be a mathematically sound approach for modeling two-dimensional potential problems . The foundations of the CVBEM method rests in complex variable theory, namely, the Cauchy integral formula. It tells us that if a function, ω, is analytic within and…
Karl K. Brustad
Imagine you are standing at a point x on a ledge [−1, 1]. A number −1 ≤ r ≤ 1 is picked at random. If it is positive you get to walk r metres to the right, but if it is negative you have to a take a step |r| metres towards, and perhaps over, the edge at x = −1. The process is repeated until you either have reached…
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…
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…
Shixiong Wang, Jianhua He, Chen Wang, Xitong Li
Many Engineering Problems could be mathematically described by Final Value Problem, which is the inverse problem of Initial Value Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the differences and relations between initial and final value problems. The more…
J.L. Gracia, Eugene O’Riordan
Numerical approximations to the solutions of three different problem classes of singularly perturbed parabolic reaction-diffusion problems, each with a discontinuity in the boundary-initial data, are generated. For each problem class, an analytical function associated with the discontinuity in the data, is identified.…
Saima Bibi, Syeda Tehmina Ejaz
In numerical methods, fine mesh sizes are often necessary to obtain highly accurate solutions of the differential equations and this increases the memory consumption and decreases the efficiency of the calculation. This paper presents a subdivision collocation algorithm of time-fractional advection diffusion equation…
Authors not listed
The polarizable continuum model (PCM) is a computationally efficient way to incorporate dielectric boundary conditions into electronic structure calculations, via a boundary-element reformulation of Poisson's equation. This transformation is only rigorously valid for an isotropic dielectric medium. To simulate…
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…
Fabian Fröhlich, Peter K. Sorger
Ordinary differential equation (ODE) models are widely used to describe biochemical processes, since they effectively represent mass action kinetics. Optimization-based calibration of ODE models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a…
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…