An Approximation Solution of Linear Differential Equation using Kantorovich Methods

Q3 Engineering

WSEAS Transactions on Applied and Theoretical Mechanics Pub Date : 2023-03-16 DOI:10.37394/232011.2023.18.2

W. A. Ahmood, Marwa Mohamed Ismaeel

引用次数: 0

Abstract

In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.

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用Kantorovich方法近似解线性微分方程

在我们的工作中，我们构造了一种数值近似方法来处理线性微分方程的近似。我们解释了投影法的一般框架，这有助于澄清坎托罗维奇方法的基本思想。应用迭代投影法，给出了构造解对精确解的收敛性定理。另外，前面遇到的大多数表达式都可以用来定义函数。这里有一些插图。通过研究函数关系的图，可以了解到关于函数关系的大量信息。第4节的基本目标是熟悉一些重要函数的图形，并开发基本的绘图程序。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Applied and Theoretical Mechanics Engineering-Computational Mechanics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Applied and Theoretical Mechanics publishes original research papers relating to computational and experimental mechanics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with fluid-structure interaction, impact and multibody dynamics, nonlinear dynamics, structural dynamics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.