An iterative method for the approximate solution of differential-difference equations with a small retardation

1977 ◽  
Vol 17 (4) ◽  
pp. 135-150
Author(s):  
Yu.P. Boglaev
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Difference Equations

scholarly journals Iterative approximation of fixed points of generalized weak Presic type k-step iterative method for a class of operators

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 713-724 ◽  
Author(s):  
Mujahid Abbas ◽  
Dejan Ilic ◽  
Talat Nazir
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Difference Equations ◽  
Global Attractivity ◽  
Iterative Approximation ◽  
Type K ◽  
Matrix Difference Equations

In this paper, we study the convergence of the generalized weak Presic type k-step iterative method for a class of operators f:Xk ? X satisfying Presic type contractive conditions. We also obtain the global attractivity results for a class of matrix difference equations.

Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain

2019 ◽  
Vol 19 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Ekaterina A. Muravleva ◽  
Ivan V. Oseledets
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Frequency Domain ◽  
Linear Systems ◽  
Stokes Problem ◽  
Inverse Operator ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation ◽  
Reduced Complexity

AbstractIn this paper we propose an efficient algorithm to compute low-rank approximation to the solution of so-called “Laplace-like” linear systems. The idea is to transform the problem into the frequency domain, and then use cross approximation. In this case, we do not need to form explicit approximation to the inverse operator, and can approximate the solution directly, which leads to reduced complexity. We demonstrate that our method is fast and robust by using it as a solver inside Uzawa iterative method for solving the Stokes problem.

scholarly journals Inversion of the Laplace Transform from the Real Axis Using an Adaptive Iterative Method

2009 ◽  
Vol 2009 ◽  
pp. 1-38 ◽  
Author(s):  
Sapto W. Indratno ◽  
Alexander G. Ramm
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Laplace Transform ◽  
Real Axis ◽  
Quadrature Formula ◽  
Compact Support ◽  
Unknown Function ◽  
Stopping Rule ◽  
The Real ◽  
The Laplace Transform

A new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to , are proposed in this paper.

Optimal Finite Analytic Methods

1982 ◽  
Vol 104 (3) ◽  
pp. 432-437 ◽  
Author(s):  
R. Manohar ◽  
J. W. Stephenson
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Linear Combination ◽  
Difference Equations ◽  
New Method ◽  
Linear Partial Differential Equations ◽  
Finite Difference Equations

A new method is proposed for obtaining finite difference equations for the solution of linear partial differential equations. The method is based on representing the approximate solution locally on a mesh element by polynomials which satisfy the differential equation. Then, by collocation, the value of the approximate solution, and its derivatives at the center of the mesh element may be expressed as a linear combination of neighbouring values of the solution.

An iterative method to solve a nonlinear matrix equation

2016 ◽  
Vol 31 ◽  
pp. 620-632
Author(s):  
Peng Jingjing ◽  
Liao Anping ◽  
Peng Zhenyun
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Matrix Equation ◽  
Closed Ball ◽  
Open Ball ◽  
Nonlinear Matrix Equation ◽  
Initial Matrix ◽  
Convergence Results ◽  
The Matrix ◽  
Nonlinear Matrix

n this paper, an iterative method to solve one kind of nonlinear matrix equation is discussed. For each initial matrix with some conditions, the matrix sequences generated by the iterative method are shown to lie in a fixed open ball. The matrix sequences generated by the iterative method are shown to converge to the only solution of the nonlinear matrix equation in the fixed closed ball. In addition, the error estimate of the approximate solution in the fixed closed ball, and a numerical example to illustrate the convergence results are given.

scholarly journals Application of the Variational Iteration Method to Strongly Nonlinear -Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hsuan-Ku Liu
Keyword(s):  
Approximate Solution ◽  
Time Scales ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Series Solutions ◽  
Nonlinear Difference Equations ◽  
Strongly Nonlinear ◽  
Variational Iteration

The theory of approximate solution lacks development in the area of nonlinear -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two -polynomials are not easily found. In this paper, the formula for the multiplication of two -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear -difference equations.

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