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273854

Exact and Approximate to Exact Methods for Solution Linear Boundary Value Problems Using Laplace Transform.

Article

Last updated: 28 Dec 2024

OverviewSimilar Items

Subjects

-

Tags

General Engineering

Abstract

 It is a new method, a mixture of numerical and exact methods, each of
which has a role to obtain the solution. It is known that the Laplace transforms
method gives a closed-form for initial value problems but in the present study, we
were able to use it with the aid of high-accurate numerical methods to solve linear
boundary value problems. The novelty of the present method that it is converted
Linear Boundary Value Problems to initial Value Problems using accurate
numerical methods and then uses Laplace transforms method to find approximate
to the exact solution. Approximate to Exact Method (AEM) is an algorithm, with a
very strong accuracy that approaches the exact solution because it is a mixture of
numerical methods of very high accuracy with a closed-form method. The
uniqueness, convergence, and stability of the new technique are verified and tested
by comparisons with a fourth-order accurate finite difference (FOFDM) solution.

DOI

10.21608/msaeng.2022.273854

Keywords

Exact method, AEM, BVP, Laplace transform

Authors

First Name

Hussein Abd Allah

Last Name

Soliman

MiddleName

-

Affiliation

Department of Basic Science, Engineering Division, International Academy for Engineering and Media Science

Email

hussein.abdallah.soliman@iaems.edu.eg

City

-

Orcid

0000-0001-5930-6192

Volume

1

Article Issue

4

Related Issue

38146

Issue Date

2022-12-01

Receive Date

2022-12-12

Publish Date

2022-12-01

Page Start

113

Page End

125

Print ISSN

2812-5339

Online ISSN

2812-4928

Article File

MSAENG_Volume 1_Issue 4_Pages 113-125.pdf

PDF . 275.5kB

Link

https://msaeng.journals.ekb.eg/article_273854.html

Detail API

https://msaeng.journals.ekb.eg/service?article_code=273854

Order

273,854

Type

Original Article

Type Code

2,183

Publication Type

Journal

Publication Title

MSA Engineering Journal

Publication Link

https://msaeng.journals.ekb.eg/

MainTitle

Exact and Approximate to Exact Methods for Solution Linear Boundary Value Problems Using Laplace Transform.

Details

Type

Article

Created At

23 Jan 2023