Related papers: An Alternative Method for the Undetermined Coeffic…
The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by…
Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…
In this article we consider the problem of approximative solution of linear differential equations $y'+p(x)y=q(x)$ with discontinuous coefficients $p$ and $q$. We assume that coefficients of such equation are Henstock integrable functions.…
We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson…
We give a simple solution of the equation d/dx(pdu/dx)+qu=cu whenever a nontrivial solution of d/dx(pdu/dx)+qu=0 is known. The method developed for obtaining this result is based on the theory of pseudoanalytic functions and their…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
The method to solve inhomogeneous linear differential equations that is usually taught at school relies on the fact that the right hand side function is the product of a polynomial and an exponential and that the linear spaces of those…
In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
A meromorphic solution of a complex linear differential equation (with meromorphic coefficients) for which the value zero is the only possible finite deficient/deviated value is called a standard solution. Conditions for the existence and…
In this paper, approximate analytical solutions of nonlinear Emden-Fowler type equations are obtained by the differential transform method (DTM). The DTM is a numerical as well as analytical method for solving integral equations, ordinary…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…