The Generalized Riemann Problem for Linear Differential Equations and the Allied Problems for Linear Difference and q-Difference Equations

1913 ◽  
Vol 49 (9) ◽  
pp. 521 ◽  
Author(s):  
George D. Birkhoff
Keyword(s):  
Differential Equations ◽  
Riemann Problem ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Generalized Riemann Problem ◽  
Linear Differential

scholarly journals Further study on solutions of some non-linear homogeneous differential equations in connection to Brück conjecture

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
DILIP CHANDRA PRAMANIK ◽  
KAPIL ROY
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Linear Complex ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Sharing Function ◽  
Linear Differential ◽  
Brück Conjecture

In this paper, using the theory of complex differential equations, we study the solution of some non-linear complex differential equations in connection to Brück conjecture which generalized some earlier results due to Pramanik, D. C. and Biswas, M., On solutions of some non-linear differential equations in connection to Bruck conjecture, Tamkang J. Math., 48 (2017), No. 4, 365–375; and Wang, H., Yang, L-Z. and Xu, H-Y., On some complex differential and difference equations concerning sharing function, Adv. Diff. Equ., 2014, 2014:274.

On the Operational Solution of Linear Finite Difference Equations

1931 ◽  
Vol 27 (1) ◽  
pp. 26-36 ◽  
Author(s):  
L. M. Milne-Thomson
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Operational Method ◽  
Finite Difference Equations ◽  
Operational Solution ◽  
Linear Differential

The application of the operational method of Oliver Heaviside to the solution of linear differential equations has been fully described in a recent Cambridge Tract by Dr H. Jeffreys.

The function and associated polynomials

1951 ◽  
Vol 47 (2) ◽  
pp. 309-314 ◽  
Author(s):  
D. F. Lawden
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Linear Difference Equations ◽  
Transform Method ◽  
Associated Polynomials ◽  
The Laplace Transform ◽  
Linear Differential ◽  
Image Position

A transform method for the solution of linear difference equations, analogous to the method of the Laplace transform in the field of linear differential equations, has been described by Stone (1). The transform u(z) of a sequence un is defined by the equation

scholarly journals Direct integration of systems of linear differential and difference equations

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1453-1461
Author(s):  
Syrgak Kydyraliev ◽  
Anarkul Urdaletova
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Main Idea ◽  
Euler Method ◽  
Linear Differential Equations ◽  
Combination Method ◽  
Direct Integration ◽  
Matrix Eigenvalues ◽  
Linear Differential ◽  
System Variables

Traditionally the Euler method is used for solving systems of linear differential equations. The method is based on the use of eigenvalues of a system?s coefficients matrix. Another method to solve those systems is the D?Alembert integrable combination method. In this paper, we present a new method for solving systems of linear differential and difference equations. The main idea of the method is using the coefficients matrix eigenvalues to find integrable combinations of system variables. This method is particularly advantageous when nonhomogeneous systems are considered.

Sign in / Sign up

Export Citation Format

Share Document