20 papers · ranked by Valyu relevance
D. Levi, Miguel Á. Rodríguez
The Jacobi Last Multiplier (JLM) [1, 7] plays, in first order linear partial differential equations, a role similar to the integrating factor in first order ordinary differential equations. If one can guess a JLM, it is possible to find the general solution of the equation, or for equations with more than two variables…
Youssouf Akrour, Nouressadat Touafek, Yacine Halim
Solving difference equations and their systems is a subject that attract the attention of several researchers and a big number of papers is devoted to this line of research where various models are proposed. We can consult for example the papers [1]- [26], for some concrete models of such equations and systems where…
Nashat Faried, Enas M Shehata, Rasha M El Zafarani
In this paper, we prove the existence and uniqueness of solutions of the β-Cauchy problem of second order β-difference equations a_{0}tD_{\beta}^{2}yt+a_{1}tD_{\beta}yt+a_{2}tyt=bt,\quad t \in I, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…
Lucas MacQuarrie, Nasser Saad, Md. Shafiqul Islam
Hahn’s difference operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$\end{document} D q …
Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Wasfi Shatanawi
'Wasfi Shatanawi'] An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the…
Petro Kolosov
| 1. | Introduction | 1 | | --- | --- | --- | | 2. | Definitions for discrete distribution | 3 | | 3. | Difference and derivative of power function | 4 | | 4. | Difference of polynomials | 6 | | 5. | Relation with Partial derivatives | 8 | | 6. | Relations between finite differences | 10 | | 7. | The error of…
Hailu Bikila Yadeta
where y(x) ∈ R n, m1, m2, ..., mk ≥ 0, and µ1(x), µ2(x), ..., µk(x) ≥ 0. Remark 1.2. In most textbooks, in place of the scalar variable x that we use here, the scalar variable t which commonly signify time in time-varying process is used. We use x as an independent scalar variable and y as unknown scalar variable that…
Georgii Khantarzhiev
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the n-th derivative of a function with the difference sequence for the values of this function. Also the results of difference sequences theory helps to discover…
Alexander Pikovski, Dennis Salahub
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue…
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…
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…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Kai Trepka
Building models of organismal growth enables predictions of natural variability and responses to perturbations. Complex systems such as animal pattern development and bacterial colonies can be modeled numerically using a reaction-diffusion system with relatively few factors and yield qualitatively accurate results…
Alberto Contreras-Cristan, Jose Gonzalez-Barrios, Raul Rueda
In this work, we illustrate and explore the use of Taylor series as solutions of differential equations. For a large a number of classes of differential equations in the literature, there are plenty of sources where the well known Taylor Series Method is used to approximate the solution, but here we are focused in…
Rémi Fay, Julien Martin, Floriane Plard
Any average pattern observed at the population level may confound two different processes: the within-individual process and the between-individual process. Separating within- from between-individual patterns is critical for our understanding of ecological processes and evolutionary dynamics. The within-individual…
Simone Pigolotti
Cell division times in microbial populations display significant fluctuations. These fluctuations impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical…
Alexandr N. Tetearing
The numerical models of populations behaviour, simulated under changing condition of populations interaction (the hungry or full-fed populations, the existence of persons in the personal areas or in the common territory), demonstrate the increase, reduction or damping of oscillations amplitude, that corresponds…
Johannes G. Borgqvist, Philip Gerlee, Carl Lundholm
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit…
V. N. Krishnachandran
| 1 | Introduction | 3 | | --- | --- | --- | | 2 | The date of birth of differential equations | 3 | | 3 | Some earlier ideas: Newton's approach | 4 | | | 3.1 Newton's classification of differential equations | 4 | | | 3.2 Newton's method of solution | 4 | | 4 | First order differential equations | 5 | | | 4.1…
Authors not listed
How to accelerate a reaction has been a critical question in physical organic chemistry, eliciting multiple models describing the interplay between kinetics and thermodynamic driving forces. However, existing models often come with inevitable limitations: valid only within finite thermodynamic ranges, rely on heavy…