A Comparative Analysis of Two Semi Analytic Approaches in Solving Systems of First-Order Differential Equations

Khadeejah  James Audu; Onıfade Babatunde

Makale detayları

A Comparative Analysis of Two Semi Analytic Approaches in Solving Systems of First-Order Differential Equations

Yazarlar:

Khadeejah James Audu | Onıfade Babatunde

Yayıncı:

Burdur Mehmet Akif Ersoy University

Ana Başlıklar:

Modelling and Simulation

Dergi:

Scientific Journal of Mehmet Akif Ersoy University Vol.7 Issue 1, pp.8-24

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001321741

pISSN:

2651-3722

Anahtar kelimeler:

Özet:

 The resolution of systems of first-order ordinary differential equations ODEs stands as a pivotal pursuit with extensive implications across scientific and engineering domains. In tackling this fundamental task, this study undertakes a rigorous comparative assessment of two semi-analytic methodologies, the Variational Iterative Method VIM and the New Iterative Method NIM. Motivated by the need to address a critical research gap, our investigation delves into these approaches relative merits and demerits. Firstly, it conducts a comprehensive examination of VIM, a well-established method, juxtaposed with NIM, a relatively unexplored approach, to uncover their comparative strengths and limitations. Secondly, the study contributes to the existing knowledge in numerical methods for ODEs by shedding light on essential performance characteristics, including convergence properties, computational efficiency, and accuracy, across a diverse array of ODE systems. Through meticulous numerical experimentation, we not only reveal practical insights into the efficacy of VIM and NIM but also bridge a significant knowledge gap in the field of numerical ODE solvers. Our findings highlight VIM as the more effective method, thus advancing our understanding of semi-analytic approaches for solving ODE systems and furnishing valuable guidance for practitioners and researchers in selecting the most suitable method for their specific applications.

 The resolution of systems of first-order ordinary differential equations ODEs stands as a pivotal pursuit with extensive implications across scientific and engineering domains. In tackling this fundamental task, this study undertakes a rigorous comparative assessment of two semi-analytic methodologies, the Variational Iterative Method VIM and the New Iterative Method NIM. Motivated by the need to address a critical research gap, our investigation delves into these approaches relative merits and demerits. Firstly, it conducts a comprehensive examination of VIM, a well-established method, juxtaposed with NIM, a relatively unexplored approach, to uncover their comparative strengths and limitations. Secondly, the study contributes to the existing knowledge in numerical methods for ODEs by shedding light on essential performance characteristics, including convergence properties, computational efficiency, and accuracy, across a diverse array of ODE systems. Through meticulous numerical experimentation, we not only reveal practical insights into the efficacy of VIM and NIM but also bridge a significant knowledge gap in the field of numerical ODE solvers. Our findings highlight VIM as the more effective method, thus advancing our understanding of semi-analytic approaches for solving ODE systems and furnishing valuable guidance for practitioners and researchers in selecting the most suitable method for their specific applications.

 The resolution of systems of first-order ordinary differential equations ODEs stands as a pivotal pursuit with extensive implications across scientific and engineering domains. In tackling this fundamental task, this study undertakes a rigorous comparative assessment of two semi-analytic methodologies, the Variational Iterative Method VIM and the New Iterative Method NIM. Motivated by the need to address a critical research gap, our investigation delves into these approaches relative merits and demerits. Firstly, it conducts a comprehensive examination of VIM, a well-established method, juxtaposed with NIM, a relatively unexplored approach, to uncover their comparative strengths and limitations. Secondly, the study contributes to the existing knowledge in numerical methods for ODEs by shedding light on essential performance characteristics, including convergence properties, computational efficiency, and accuracy, across a diverse array of ODE systems. Through meticulous numerical experimentation, we not only reveal practical insights into the efficacy of VIM and NIM but also bridge a significant knowledge gap in the field of numerical ODE solvers. Our findings highlight VIM as the more effective method, thus advancing our understanding of semi-analytic approaches for solving ODE systems and furnishing valuable guidance for practitioners and researchers in selecting the most suitable method for their specific applications.

 The resolution of systems of first-order ordinary differential equations ODEs stands as a pivotal pursuit with extensive implications across scientific and engineering domains. In tackling this fundamental task, this study undertakes a rigorous comparative assessment of two semi-analytic methodologies, the Variational Iterative Method VIM and the New Iterative Method NIM. Motivated by the need to address a critical research gap, our investigation delves into these approaches relative merits and demerits. Firstly, it conducts a comprehensive examination of VIM, a well-established method, juxtaposed with NIM, a relatively unexplored approach, to uncover their comparative strengths and limitations. Secondly, the study contributes to the existing knowledge in numerical methods for ODEs by shedding light on essential performance characteristics, including convergence properties, computational efficiency, and accuracy, across a diverse array of ODE systems. Through meticulous numerical experimentation, we not only reveal practical insights into the efficacy of VIM and NIM but also bridge a significant knowledge gap in the field of numerical ODE solvers. Our findings highlight VIM as the more effective method, thus advancing our understanding of semi-analytic approaches for solving ODE systems and furnishing valuable guidance for practitioners and researchers in selecting the most suitable method for their specific applications.

Makale detayları

A Comparative Analysis of Two Semi Analytic Approaches in Solving Systems of First-Order Differential Equations

Yazarlar:

Khadeejah James Audu | Onıfade Babatunde

Yayıncı:

Burdur Mehmet Akif Ersoy University

Ana Başlıklar:

Modelling and Simulation

Dergi:

Scientific Journal of Mehmet Akif Ersoy University Vol.7 Issue 1, pp.8-24

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001321741

pISSN:

2651-3722

Semi-Analytic Approaches

Systems of First-Order Differential Equations

Comparative Analysis

Analytical solution

Computational efficiency

Sayı

Makale detayları

A Comparative Analysis of Two Semi Analytic Approaches in Solving Systems of First-Order Differential Equations

Yazarlar: Khadeejah James Audu | Onıfade Babatunde

Yayıncı: Burdur Mehmet Akif Ersoy University

Ana Başlıklar: Modelling and Simulation

Dergi: Scientific Journal of Mehmet Akif Ersoy University Vol.7 Issue 1, pp.8-24

Belge Tipi: Makale

Yayın Tarihi: 6/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001321741

pISSN: 2651-3722

Semi-Analytic Approaches

Systems of First-Order Differential Equations

Comparative Analysis

Analytical solution

Computational efficiency

Sayı

Yazarlar:

Khadeejah James Audu | Onıfade Babatunde

Yayıncı:

Burdur Mehmet Akif Ersoy University

Ana Başlıklar:

Modelling and Simulation

Dergi:

Scientific Journal of Mehmet Akif Ersoy University Vol.7 Issue 1, pp.8-24

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001321741

pISSN:

2651-3722