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Ordinary Differential Equations
In this chapter we illustrate the implementation of the simplest numerical methods that help solving Initial Value Problems associated to Ordinary...
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Ordinary Differential Equations
Ordinary differential equation of first and second order are discussed, as well as systems of two ordinary differential equations.
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Automatically discovering ordinary differential equations from data with sparse regression
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science....
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Existence of solutions of a system of two ordinary differential equations with a modular–cubic type nonlinearity
AbstractWe use asymptotic analysis to study the existence of solutions of a one-dimensional nonlinear system of ordinary differential equations...
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A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations
In this paper, we present a method for deriving quantifiers of the extended Prelle–Singer (PS) method using Darboux polynomials for third-order...
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On Specific Features of an Approach Based on Feedforward Neural Networks to Solve Problems Based on Differential Equations
AbstractTo date, a multitude of methods have been developed for numerical solution of problems based on ordinary differential equations (ODEs) and...
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Differential Equations
Many natural laws in physics and engineering are formulated by equations involving derivatives or differentials of physical quantities.
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Naïve Perturbation Method for Solving Ordinary Differential Equations and Notion of Secular Terms
Using simple differential equations, we introduce the notion of secular terms, and then demonstrate that secular terms are to appear in general in...
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Solution Stability of Delay Differential Equations in Banach Spaces
AbstractThe Lyapunov stability of steady-state solutions to nonlinear differential equations with time-dependent operators and time-dependent delay...
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Differential and Difference Equations as Dynamical Systems
We introduce the concept of a dynamical system and review the basic results and the terminology of the qualitative theory of differential and...
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On Bäcklund transformations for some second-order nonlinear differential equations
AbstractWe obtain second-order nonlinear differential equations (and the associated Bäcklund transformations) with an arbitrary analytic function...
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Algorithm for differential equations for Feynman integrals in general dimensions
We present an algorithm for determining the minimal order differential equations associated with a given Feynman integral in dimensional or analytic...
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Mathematical Preliminary II: Theory of Second Order Differential Equations
For the benefit of students not familiar with theory of second order differential equations, it is provided together with theory of boundary value...
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Lie groups, singularities and solutions of nonlinear partial differential equations
It is shown how Lie group and Lie algebra theory can be used to solve partial differential equations. A method for calculating the symmetry group of...
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Partial Differential Equations of Mathematical Physics
If an unknown function of several variables and its partial derivatives are combined in an equation, the latter is called a partial differential...
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Some new methods for studying boundary value problems for general partial differential equations
AbstractWe consider methods for studying boundary value problems for linear partial differential equations in a domain regardless of the type of...
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Real time lattice correlation functions from differential equations
We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian...
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Modular differential equations with movable poles and admissible RCFT characters
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the...
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A quantum algorithm for linear differential equations with layerwise parameterized quantum circuits
Solving linear differential equations is a common problem in almost all fields of science and engineering. Here, we present a variational algorithm...
