Linear differential equations modeled after hyperquadrics

Approximately $n$-order linear differential equations

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Formally Analyzing Continuous Aspects of Cyber-Physical Systems Modeled by Homogeneous Linear Differential Equations

Traditionally, the continuous aspects of cyber-physical systems (CPS), usually modeled by differential equations, are analyzed using paper-and-pencil proof methods, computer based numerical methods or computer algebra systems. All these methods are error-prone and thus the analysis cannot be termed as accurate, which poses a serious threat to the accuracy of the cyber-physical systems. To guara...

Linear Differential Equations

Linear Differential Equations

1. Linearity and Continuity 1.1 Continuity 1.2 Linearity 1.3 Perturbation theory and linearity 1.4 Axiomatically linear equations 1.4.1 Fields, Maxwell equations 1.4.2 Densities on phase space in classical physics 1.4.3 Quantum mechanics and Schrödinger equation 2. Examples 2.1 Ordinary differential equations 2.2 The Laplace equation 2.3 The wave equation 2.4 The heat equation and Schrödinger e...

Reversible linear differential equations

Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism σ : Γ → Γ is called a symmetry of ∇ if the pull-back bundle and the pull-back connection can be identified with ∇. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group,...