Related papers: Solving Linear Differential Equations: A Novel App…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
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…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…