Numerical and analytical solutions of an ODE: Strengths and weaknesses of the analytical series solution

C. Ahmed Basha; G. Rahamathunissa; S. Sivakumar; Chang Woo Lee

doi:10.1016/j.apm.2011.07.025

Numerical and analytical solutions of an ODE: Strengths and weaknesses of the analytical series solution

C. Ahmed Basha
, G. Rahamathunissa
, S. Sivakumar
, Chang Woo Lee

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The analytical solution for a nonlinear ordinary differential equation was obtained but was only applicable for lower input parameters. A numerical solution for the same equation which provided good results for all input parameters was also obtained. Since the analytical solution contained an infinite series, the solution depended on the number of terms used in the series, resulting in failure for certain input parameters at low time values.

Original language	English
Pages (from-to)	618-625
Number of pages	8
Journal	Applied Mathematical Modelling
Volume	36
Issue number	2
DOIs	https://doi.org/10.1016/j.apm.2011.07.025
Publication status	Published - Feb 2012

Bibliographical note

Funding Information:
One of the authors (CAB) thanks the Korean Federation of Science and Technology Societies for a grant funded by the Korean government (MEST, Basic Research Promotion Fund) (No.101S-4-3-0270) for the financial support of this work.

Keywords

Analytical solution
Non-linear differential equation
Numerical solution
Series

Access to Document

10.1016/j.apm.2011.07.025

Cite this

@article{59bfccadd09046889a161a4f2ebe2184,

title = "Numerical and analytical solutions of an ODE: Strengths and weaknesses of the analytical series solution",

abstract = "The analytical solution for a nonlinear ordinary differential equation was obtained but was only applicable for lower input parameters. A numerical solution for the same equation which provided good results for all input parameters was also obtained. Since the analytical solution contained an infinite series, the solution depended on the number of terms used in the series, resulting in failure for certain input parameters at low time values.",

keywords = "Analytical solution, Non-linear differential equation, Numerical solution, Series",

author = "\{Ahmed Basha\}, C. and G. Rahamathunissa and S. Sivakumar and Lee, \{Chang Woo\}",

note = "Funding Information: One of the authors (CAB) thanks the Korean Federation of Science and Technology Societies for a grant funded by the Korean government (MEST, Basic Research Promotion Fund) (No.101S-4-3-0270) for the financial support of this work.",

year = "2012",

month = feb,

doi = "10.1016/j.apm.2011.07.025",

language = "English",

volume = "36",

pages = "618--625",

journal = "Applied Mathematical Modelling",

issn = "0307-904X",

publisher = "Elsevier Inc.",

number = "2",

}

TY - JOUR

T1 - Numerical and analytical solutions of an ODE

T2 - Strengths and weaknesses of the analytical series solution

AU - Ahmed Basha, C.

AU - Rahamathunissa, G.

AU - Sivakumar, S.

AU - Lee, Chang Woo

N1 - Funding Information: One of the authors (CAB) thanks the Korean Federation of Science and Technology Societies for a grant funded by the Korean government (MEST, Basic Research Promotion Fund) (No.101S-4-3-0270) for the financial support of this work.

PY - 2012/2

Y1 - 2012/2

N2 - The analytical solution for a nonlinear ordinary differential equation was obtained but was only applicable for lower input parameters. A numerical solution for the same equation which provided good results for all input parameters was also obtained. Since the analytical solution contained an infinite series, the solution depended on the number of terms used in the series, resulting in failure for certain input parameters at low time values.

AB - The analytical solution for a nonlinear ordinary differential equation was obtained but was only applicable for lower input parameters. A numerical solution for the same equation which provided good results for all input parameters was also obtained. Since the analytical solution contained an infinite series, the solution depended on the number of terms used in the series, resulting in failure for certain input parameters at low time values.

KW - Analytical solution

KW - Non-linear differential equation

KW - Numerical solution

KW - Series

UR - https://www.scopus.com/pages/publications/80053564611

U2 - 10.1016/j.apm.2011.07.025

DO - 10.1016/j.apm.2011.07.025

M3 - Article

AN - SCOPUS:80053564611

SN - 0307-904X

VL - 36

SP - 618

EP - 625

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - 2

ER -

Numerical and analytical solutions of an ODE: Strengths and weaknesses of the analytical series solution

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this