Modeling Examples for Models Splitting Ideas Theory Chapter 2: Decompositon and Discretization Differential Equations Operator Equations Chapter 3: Extensions Extensions Iterative Splitting Methods as Modified Decomposition Schemes

2011 ◽  
pp. 29-31
Keyword(s):  
Differential Equations ◽  
Splitting Methods ◽  
Operator Equations ◽  
Decomposition Schemes

scholarly journals On the solvability of nonlinear noncompact operator equations

1987 ◽  
Vol 43 (1) ◽  
pp. 103-126 ◽  
Author(s):  
E. U. Tarafdar ◽  
H. B. Thompson ◽  
R. O. Vyborny
Keyword(s):  
Differential Equations ◽  
Operator Equations

AbstractThe notion of (p, k)-epi mappings is introduced. The properties of such mappings are studied and the results obtained are applied to some differential equations.

scholarly journals Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hua Su
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Iterative Solution ◽  
Order Method ◽  
Operator Equations ◽  
Abstract Operator ◽  
Uniqueness Of A Solution

In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

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