25 papers · ranked by Valyu relevance
Megan Morrison, Sonja Petrović
Many important systems across biology, engineering, physics, and economics are characterized by polynomial ordinary differential equations (ODEs), yet analytical solutions are rare. We develop a framework for identifying and solving a broad class of two-dimensional quadratic ODEs using linear rational Koopman…
Sepideh Sharif, Chihiro Hasegawa, Stephen B. Duffull
Nonlinear ordinary differential equations (ODEs) are common in pharmacokinetic-pharmacodynamic systems. Although their exact solutions cannot generally be determined via algebraic methods, their rapid and accurate solutions are desirable. Thus, numerical methods have a critical role. Inductive Linearization was…
Hina M. Dutt, Asghar Qadir
Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order linearizable ODEs and then applying the Ibragimov and Meleshko linearization test for…
R. Mohanasubha, Jane H. Sheeba, V. K. Chandrasekar, M. Senthilvelan + 1 more
'M. Lakshmanan'] Abstract. In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations (ODEs) with…
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…
V. Murugesh, M. Priyadharshini, Yogesh Kumar Sharma, Umesh Kumar Lilhore + 4 more
'Umesh Kumar Lilhore' 'Roobaea Alroobaea' 'Hamed Alsufyani' 'Abdullah M. Baqasah' 'Sarita Simaiya'] In this paper, the author introduces the Neural-ODE Hybrid Block Method, which serves as a direct solution for solving higher-order ODEs. Many single and multi-step methods employed in numerical approximations lose their…
Per Kristen Jakobsen
It is now finally time to start solving differential equations using asymptotic expansions. Let us start with a simple boundary value problem for a first order ordinary differential equation. Consider the following boundary value problem (6-1)$y^{\prime}(x)+y(x)+\varepsilon y^{2}(x)=x,\ \ 0<x<1,$ (6-2)$y(1)=1,\tag{60}$…
M. G. Blyth, Ludovic Renson, Lucia Marucci
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex task, such that we have little choice but to approach the problem with…
D. T. Pham, Z. E. Musielak
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and…
Authors not listed
Accurate modeling of drug concentration--time (C--t) profiles is central to pharmacokinetics (PK) and plays a critical role in both early-stage compound selection and late-stage individualized dosing. Traditional PK model offer mechanistic interpretability but often rely on rigid assumptions, extensive…
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…
Shariful Islam, Bishnupada Halder, Ahmed Refaie Ali
In this study, the uses of unified method for finding solutions of a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the…
M Ali Akbar, Norhashidah Hj Mohd Ali, Syed Tauseef Mohyud-Din
Title: PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik
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…
А. В. Аксенов, Andrei D. Polyanin
The paper describes a number of simple but quite effective methods for constructing exact solutions of nonlinear partial differential equations, that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (i) simple exact solutions can serve to construct more complex…
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…
Aleksandr Fedorov, Anna Perechodjuk, David Linke
Artificial neural networks (ANNs) are powerful tools for solving a wide range of tasks in fundamental and applied science. However, training and building reliable ANN models requires a lot of data which so far hinders their wider application in kinetic modelling where typically only small (experimental) datasets are…
Bartosz Prokop, Lendert Gelens
Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally…
Rimsha Ansar, Muhammad Abbas, Homan Emadifar, Tahir Nazir + 2 more
'Ahmed S. M. Alzaidi' 'Muhammad Aqeel'] The aim of the present study is to identify multiple soliton solutions to the nonlinear coupled Broer-Kaup-Kupershmidt (BKK) system, including beta, conformable, local-fractional, and M-truncated derivatives. The coupled Broer-Kaup-Kupershmidt system is employed for modelling…
O. González-Gaxiola
The Kundu-Eckhaus equation is a nonlinear partial differential equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics. In spite of its importance, exact solution to this nonlinear equation are rarely found in literature. In this work, we solve this equation and…
Santosh Manicka, Kathleen Johnson, Michael Levin, David Murrugarra
The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed ‘regulatory nonlinearity’, we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear…
Evgeni V. Nikolaev, Sahand Jamal Rahi, Eduardo D. Sontag
This paper uncovers a remarkable behavior in two biochemical systems that commonly appear as components of signal transduction pathways in systems biology. These systems have globally attracting steady states when unforced, so they might have been considered “uninteresting” from a dynamical standpoint. However, when…
Authors not listed
This paper presents the Multi Cell-line Kinetic Model (MCKM), a novel generalised kinetic mechanistic model specifically tailored for Ambr15™ fed-batch cultivations of multiple Chinese Hamster Ovary (CHO) cell lines producing different recombinant monoclonal antibodies (mAbs). Unlike traditional models that requires…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…