Search · four archives
Search · four archives
24 papers · ranked by Valyu relevance
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…
Rajnish Kumar Jha
In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential equation, which happens to be a Riccati Equation. We also derive other results based…
Артем Пономаренко
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of terms in the equation. Here we carry out this only for equations of the first and…
Swarup Poria, Aman Dhiman
The method of variation of parameter (VOP) for solving linear ordinary differential equation is revisited in this article. Historically, Lagrange and Euler explained the method of variation of parameter in the context of perturbation method. In this article, we explain the construction of particular solutions of a…
K. V. Zhukovsky
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent…
Margaret P. Chapman, Claire J. Tomlin
Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model…
Supaporn Suksern, Sergey V. Meleshko
The problem of linearization of a nonlinear ordinary differential equation has attracted a lot of attention of scientists. The first linearization problem for ordinary differential equations was solved by S.Lie [1]. He found the general form of all ordinary differential equations of second-order which can be reduced to…
Heather A. Harrington, Robert A. Van Gorder
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where…
Daniele Pessina, Tony Tian, Oliver Watson, Jerry Y. Heng + 1 more
Modelling complex crystallisation processes remains challenging due to limited experimental datasets, high measurement noise, and the need for generalisability across varying operating conditions. Neural Ordinary Differential Equations (NODEs) and transfer learning (TL) offer promising tools to overcome these…
Jasmine A. Nirody, Padmini Rangamani
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains are now widely acknowledged as key features of biochemical signal transduction.…
Jianfeng Wang
In this paper we discuss the first order partial differential equations resolved with any derivatives. At first, we transform the first order partial differential equation resolved with respect to a time derivative into a system of linear equations. Secondly, we convert it into a system of the first order linear…
Domagoj Dorešić, Stephan Grein, Jan Hasenauer
Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. The parameters of these models are commonly estimated from experimental data. Yet, experimental data generated from different techniques do not provide direct information about the state of the…
Authors not listed
Redox-mediated flow batteries (RMFBs) promise increased energy density through the incorporation of solid active materials into the external tanks, but the operation and design of these devices is challenged by kinetic, thermodynamic, and transport complexities introduced by the solid-mediator reactions. Here, we…
Marta Leocata, J. C. L. Alfonso, Nikos I. Kavallaris, Haralampos Hatzikirou
Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is non-linearly integrated in the corresponding evolution term, typically termed as random ordinary differential equations (RODEs).…
Uriel Filobello-Nino, Hector Vazquez-Leal, Juan Cervantes-Perez, Brahim Benhammouda + 7 more
'Brahim Benhammouda' 'Agustin Perez-Sesma' 'Luis Hernandez-Martinez' 'Victor Manuel Jimenez-Fernandez' 'Agustin Leobardo Herrera-May' 'Domitilo Pereyra-Diaz' 'Antonio Marin-Hernandez' 'Jesus Huerta Chua'] This article proposes Laplace Transform Homotopy Perturbation Method (LT-HPM) to find an approximate solution for…
Stefano Giampiccolo, Giovanni Iacca, Luca Marchetti
Dynamical systems play a central role across the quantitative sciences, offering a powerful mathematical framework to describe, analyze, and predict the evolution of complex processes over time. In Systems Biology, dynamical systems provide a foundation for modeling and predicting the intricate behaviors of biological…
Timilehin Kingsley Akinfe, Adedapo Chris Loyinmi
In this research, an unrivalled hybrid scheme which involves the coupling of the new Elzaki integral transform (an improved version of Laplace transform) and a modified differential transform called the projected differential transform (PDTM) have been implemented to solve the generalized Burgers-Fisher's equation…
Authors not listed
We develop a control-oriented model for manipulating calcium carbonate (CaCO3) precipitation through pH and/or dissolved CO2(aq) adjustments in a semi-batch process. We present two open-loop control strategies: first, a closed-form optimal control solution derived via Pontryagin’s Minimum Principle; and second, an…
D.T. Pham, Z.E. Musielak
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Andrew McCluskey
The use of mathematical transformations to reduce non-linear functions to linear problems, which can be tackled with analytical linear regression, is commonplace in the chemistry curriculum. The linearization procedure, however, assumes an incorrect statistical model for real experimental data; leading to biased…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Praveen Agarwal, Carlo Cattani + 3 more
'Carlo Cattani' 'Thiab Taha' 'Shaher Momani' 'Juan García Guirao'] We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…