Nature

Inverse Problems in Spectral Theory and Differential Operators

Inverse problems in spectral theory address the challenge of reconstructing differential operators from observed spectral data. This field, rich in both theoretical and applied mathematics, underpins ...
Scientific Research Publishing

Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions ()

Linear Periodic Differential Equations (PDDEs) have been of importance for studying problems of vibration, mechanics, astronomy, electric circuits, biology among others in [1] several examples of ...
Scientific Research Publishing

Weidmann, J. (1987) Spectral Theory of Ordinary Differential Operator, Lecture Notes in Mathematics, Vl 1258. Springer-Verlag, Berlin.

ABSTRACT: In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three ...
Europe PMC

Numerical solution of linear integro-differential equations by using generalized Bernstein operator collocation method

In this paper, we use the generalized Bernstein operator collocation method to compute weak singular kernel differential integral equations. We reconstruct the differential matrix form according to ...
IEEE

Operator Algebra for Differential Systems

Abstract: This paper presents the development of an operator algebra for differential systems which is useful in that it allows the transmittance methods commonly applied to linear stationary systems ...
marktechpost

Newton Informed Neural Operator: A Novel Machine Learning Approach for Computing Multiple Solutions of Nonlinear Partials Differential Equations

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...