22 papers · ranked by Valyu relevance
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is…
Nikolay K. Vitanov, Quanmin Zhu, António Lopes
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins…
Zlatinka I. Dimitrova
Many complex systems are nonlinear [?]- [14]. Usually, the effects connected to nonlinearity are studied by the methods of the time series analysis or are modeled by nonlinear differential or difference equations [15] - [31]. The methodology for obtaining exact solutions of nonlinear differential equation was in…
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…
Nikolay K. Vitanov, Kaloyan N. Vitanov, José F. F. Mendes
The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple…
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as function of solutions of one or several simple equations. We show that SEsM contains…
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a version the methodology for obtaining exact solutions of nonlinear partial differential equations based on the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by Hirota [1] and the relationship used in the previous…
Elena V. Nikolova, António Lopes
We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent variables. The two composing functions are constructed as finite…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use differential equation for a special function that contains as particular cases…
Alexander Panfilov
An equation is a mathematical relationship involving unknown variables. These unknowns are usually expressed by letters 'x', 'y', however in biology we use many other letters (e.g. 'N', 'P'. 'T', 'V', etc.), which maybe somewhat related to the name of the species they describe. Solving equations means finding…
Mario Castro, Rob J. de Boer
Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. The very structure of the model limits the ability to infer numerical values for the…
Yijie Deng, Douglas Raymond Beahm, Xinping Ran, Tanner G Riley + 1 more
Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical…
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…
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…
Authors not listed
This document presents a comprehensive heuristic algorithm for the teaching and practice of fundamental inorganic chemistry in representative elements. A logical-deductive method is proposed, starting from the electronic configuration and Hund’s Maximum Multiplicity Principle to determine valence by counting unpaired…
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…
Alejandro F. Villaverde, Gemma Massonis Feixas
A recent paper (Castro M, de Boer RJ, “Testing structural identifiability by a simple scaling method”, PLOS Computational Biology, 2020, 16(11):e1008248) introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics — Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC)— which aim to quantify structural intricacies in pattern formation, enhancing…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Authors not listed
This paper introduces Post-Inspection Analysis (PIA), a concept for understanding and reverse engineering balanced equations of similar reactions. Here we explore the idea that balanced equations contain useable information observed by grouping and analysing similar equations, allowing us to uncover observations that…
Ziyue Yi
Traditional biological research heavily relies on experimental methodologies, which often lead to inefficiencies in communication and knowledge transfer. These methodologies frequently result in redundant trial-and-error experiments, posing challenges in standardizing results and impeding rapid knowledge dissemination.…
Tobias Seidel, Lena-Marie Ränger, Thomas Grützner, Michael Bortz
In this work we present a new approach that we use to simulate and optimize multiple dividing wall columns at the same time. Instead of considering all model equations as constraints and all process variables as optimization variables in a large and highly nonlinear optimization problem we only incorporate a subset of…