The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.
DIFFERENtIAl DIFFERENCE EqUAtIONS ANd APPlICA...
Difference equation - First and second-order difference equations with constant coefficients- Fibonacci sequence - Solution of difference equations - Complementary function -Particular integral by the method of undetermined coefficients - Solution of simple difference equations using Z-transform
I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential equations.
In application, differential equations are far easier to study than difference equations. I think this is because differential systems basically average everything together, hence simplifying the dynamics significantly. On the other hand, discrete systems are more realistic.
In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov-Hopf bifurcations in the differential equations and Neimark-Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark-Sacker bifurcations are less than critical times for Andronov-Hopf bifurcations but converge to them as the time step of the discretization tends to zero.
The aim of this Special Issue is to report the recent theoretical and numerical studies on fractional differential and difference equations and their life-life applications. Both original research articles, and review articles discussing the current state of the art, are welcomed.
Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations.
Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.
Advances in Continuous and Discrete Models: Theory and Modern Applications now accepts a broader range of high-quality original research and survey articles covering algorithmic and analytical developments in numerical analysis, differential equations, control, optimization, data driven modelling and scientific computing. We are also considering submissions connecting mathematical research to applications such as signal and image processing, mathematical biology and bioengineering, material science, and computer vision.
Computational and applied mathematics along with data science play a vital role in contemporary society by driving innovation. This success can be attributed to revolutionary theoretical and algorithmic developments in machine learning, data driven modeling, differential equations, numerical analysis, scientific computing, control, optimization, and computing resources together with new tools to deal with uncertainty and randomness.
An important concept in mathematics, differential and integral calculus appears naturally in numerous scientific problems, which have been widely applied in physics, chemical technology, optimal control, finance, signal processing, etc. and are modeled by ordinary or partial difference and differential equations.
In recent years, it was observed that many real-world phenomena cannot be modeled by ordinary or partial differential equations or standard difference equations defined via the classical derivatives and integrals. In fact, these problems followed the appearance of fractional calculus (fractional derivatives and integrals), intended to handle the problems for which the classical calculus was insufficient. Together with the development and progress in fractional calculus, the theory and applications of ordinary and partial differential equations with fractional derivatives became one of the most studied topics in applied mathematics. The wide application potential of fractional differential equations in many fields of science has been underlined by a huge number of articles, books, and scientific events on the subject.
Fixed point theory on the other hand, is a very strong mathematical tool to establish the existence and uniqueness of almost all problems modeled by nonlinear relations. Consequently, existence and uniqueness problems of fractional differential equations are studied by means of fixed point theory. For about a century, fixed point theory has begun to take shape, and developed rapidly. Due to its applications, fixed point theory is highly appreciated and continues to be explored. Besides, this theory can be applied in many types of spaces, such as abstract spaces, metric spaces, and Sobolev spaces. This feature of fixed point theory makes it very valuable in studying numerous problems of practical sciences modeled by fractional ordinary and partial differential and difference equations.
In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the exist...
This paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such types of equations allow the presence of two kinds of memory ef...
Some complicated events can be modeled by systems of differential equations. On the other hand, inclusion systems can describe complex phenomena having some shocks better than the system of differential equati...
In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in th...
Dr. Martin Bohner
Ordinary differential equations, dynamic equations on time scales, difference equations, Hamiltonian systems, variational analysis, boundary value problems, control theory, oscillation, analysis, fractional equations, applications to biology and economics
Dr. Martin Bohner
Ordinary differential equations, dynamic equations on time scales, difference equations, Hamiltonian systems, variational analysis, boundary value problems, control theory, oscillation, analysis, fractional equations, applications to biology and economics
Dr. John Singler
Data-driven model order reduction of partial differential equations (PDEs), computational methods for control of PDEs, applications in control theory, engineering, and the sciences
AMATH 351 Introduction to Differential Equations and Applications (3) NSc
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125 or MATH 135. Offered: AWSpS.
View course details in MyPlan: AMATH 351
AMATH 383 Introduction to Continuous Mathematical Modeling (3) NSc
Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results. Prerequisite: either AMATH 351, MATH 136, or MATH 207. Offered: AWS.
View course details in MyPlan: AMATH 383
38c6e68cf9