Related papers: Solutions of Non-Homogenous Linear Differential Eq…

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

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…

In this paper, a homogeneous system of n $\alpha$-order linear fractal differential equation is defined and the set of its fundamental solutions through the corresponding Wronskian matrix is described. Finally, the solutions of some…

In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…

In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…

An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…

In this paper, we study nonlinear differential equations of Tumura-Clunie type, $ f^n + P(z, f) = h, $ where \( n \geq 2 \) is an integer, \( P(z, f) \) is a differential polynomial in \( f \) of degree \( \gamma_P \leq n - 1 \) with small…

Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear…

We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…

This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…

In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…

We present some results in the analysis of non-compact differential equations on unbounded domains.

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…

For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic…

All the finite order entire solutions of \begin{equation*} f^n(z)+q(z)e^{Q(z)}f^{(k)}(z+c)=P(z) \end{equation*} are given, where $ q(z) $, $ Q(z), P(z) $ are polynomials, $ k $ and $ n \geq 2 $ are integers, and $ c \in \mathbb{C} \setminus…

This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order 1 + 0, also with degenerate leading coefficient. As a byproduct,…

Let $P(z)=z^{n}+a_{n-2}z^{n-2}+\cdots+a_0$ be a nonconstant polynomial and $S(z)$ be a nonzero rational function and denote $h(z)=S(z)e^{P(z)}$. Let $\theta\in(0,\pi/2n)$ be a constant and $\varepsilon>0$ be a small constant. It is shown…

In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…

Below, the explicit solution to a certain finite-difference equation is given and the required steps for derivation of these results are outlined. Everything is included as Mathematica formulae, so the notebook itself can be used for…