Related papers: A Friendly Introduction to Differential Equations
A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying…
The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by…
The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and…
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
The aim of this work is to derive new explicit solutions to the $\infty$-Laplace equation, the fundamental PDE arising in Calculus of Variations in the space $L^\infty$. These solutions obey certain symmetry conditions and are derived in…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given,…
In this book we collect many different and useful facts around gradient descent method. First of all we consider gradient descent with inexact oracle. We build a general model of optimized function that include composite optimization…
Non-holonomic constraints, both in the Lagragian and Hamiltonian formalism, are discussed from the geometrical viewpoint of implicit differential equations. A precise statement of both problems is presented remarking the similarities and…
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…
This article describes the authors' teaching experience in flipping the class of a basic undergraduate mathematics course Introductory Linear Algebra. We utilize a full-featured free electronic textbook, online lecture notes, an intranet…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…