26 papers · ranked by Valyu relevance
Davoud Mirzaei
Contents 1 An introduction to ODEs 1 1.1 Modelling with ODEs: a funny example . . . . . . . . . . . . . . . . . . . 4 1.2 Higher order ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 First order system of ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Stability of solutions . .…
Jonathan Oesterle, Nicholas Krämer, Philipp Hennig, Philipp Berens
Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic…
Yuji Masutomi, Kazuhiko Kobayashi
The photosynthesis–transpiration–stomatal conductance (A_n_–E–g_s_) model framework is widely used for estimating photosynthesis, transpiration, and stomatal conductance in plants. The model equations are solved by numerical iteration, and the converged model values are deemed the solution. However, there has been no…
Ahmet Altürk
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a…
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…
Alexander Hvatov, Tatiana Tikhonova
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of the equations, on which the convergence with a given parameter set or range is…
Malgorzata Klimek, Mariusz Ciesielski, Tomasz Blaszczyk, Praveen Agarwal + 5 more
'Praveen Agarwal' 'Carlo Cattani' 'Thiab Taha' 'Shaher Momani' 'Juan Luis García Guirao' 'António Mendes Lopes'] In this paper, we study the fractional Sturm-Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space.…
Pavel Dourbal, Mikhail Pekker
We propose a new method of numerical solution for partial differential equations. The method is based on a fast matrix multiplication algorithm developed by Dourbal [1,2]. We use a two-dimensional Poison equation for comparison of the proposed method with conventional numerical methods. We have shown that for N 5050…
Philipp Städter, Yannik Schälte, Leonard Schmiester, Jan Hasenauer + 1 more
Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when…
Byakatonda Denis
| ABSTRACT | iii | | --- | --- | | ORGANIZATION OF THE STUDY | iv | | LIST OF ABBREVIATIONS | v | | LIST OF SYMBOLS | vi | | LIST OF FIGURES | vii | | LIST OF TABLES | viii | | CHAPTER ONE 1 | | | INTRODUCTION 1 | | | 1.0 Introduction 1 | | | 1.1 Background of the study 1 | | | 1.2 Preliminaries 3 | | | 1.4 Statement…
Marius-F. Danca, Quanmin Zhu, Giuseppe Fusco, Jing Na + 1 more
In this paper, the solutions of a class of switch dynamical systems are investigated. The right-hand side of the underlying equations is discontinuous with respect to the state variable. The discontinuity is represented by jump discontinuous functions such as signum or Heaviside functions. In this paper, a novel…
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…
Zhimin Hong, Zaizai Yan, Jiao Yan, Guido Germano
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this…
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…
Özlem Ersoy Hepson, Alper Korkmaz, İdiris Dağ
In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one dimensional Boussinesq systems numerically. Two initial boundary value problems for Regularized and Classical Boussinesq systems modeling motion of traveling waves are considered. The accuracy of the method is…
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…
Kushal Dhar Dwivedi, Anup Singh
Order Differential Equations Authors: ['Kushal Dhar Dwivedi' 'Anup Singh'] Abstract In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
Pierluigi Amodio, Domenico Giordano, Felice Iavernaro, Arcangelo Labianca + 3 more
'Arcangelo Labianca' 'Monica Lazzo' 'Francesca Mazzia' 'Lorenzo Pisani'] In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…
MARCO TODISCO
Determining the distribution of multiple chemical species at equilibrium for a given system is a common problem that must be routinely addressed by scholars. While simple systems consisting of a few species and reactions can be solved manually, most of these problems require the definition and solution of higher-order…
Maud El-Hachem, Scott W. McCue, Wang Jin, Yihong Du + 1 more
The Fisher-KPP model supports travelling wave solutions that are successfully used to model numerous invasive phenomena with applications in biology, ecology, and combustion theory. However, there are certain phenomena that the Fisher-KPP model cannot replicate, such as the extinction of invasive populations. The…
Ming Yang, Louis Z. Yang
What values of relative numerical tolerance should be chosen in simulation of a deterministic model of a biochemical reaction is unclear, which impairs the modeling effort since the simulation outcomes of a model may depend on the relative numerical tolerance values. In an attempt to provide a guideline to selecting…
Michele Nottoli, Michael F. Herbst, Aleksandr Mikhalev, Abhinav Jha + 2 more
Polarizable continuum solvation models are popular in both, quantum chemistry and in biophysics, though typically with different requirements for the numerical methods. However, the recent trend of multiscale modeling can be expected to blur field-specific differences. In this regard, numerical methods based on domain…
Daniel T. Birdsell, Benjamin M. Adams, Jonathan D. Ogland-Hand, Jeffrey M. Bielicki + 2 more
Geothermal electricity generation may play a role in reducing greenhouse gas emissions and addressing climate change in a cost-effective manner. Reservoir equations for pressure and temperature must be coupled to a power cycle model to calculate electricity generation from a geothermal power plant. This work focuses on…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
Tahir Shahzad, Muhammad Ozair Ahmed, Muhammad Zafarullah Baber, Nauman Ahmed + 2 more
'Nauman Ahmed' 'Ali Akgül' 'Sayed M. El Din'] In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel…
Authors not listed
Rapid and robust simulation of chemical processes is critical to conduct process design, optimization, techno-economic analysis, and sustainability analysis. Yet, efficiently solving simulation models remains a challenge due to the highly coupled and nonlinear nature of the underlying algebraic equations that capture…