Hybrid continuous multi-step method for second order problems in ordinary differential equations

N.A.

Makale detayları

Hybrid continuous multi-step method for second order problems in ordinary differential equations

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355935

pISSN:

2980-3020

Anahtar kelimeler:

Özet:

 This study presents the development and analysis of a class of hybrid continuous methods designed for solving second-order initial value problems in ordinary differential equations. The formulation of the method is based on the application of a class of orthogonal and Chebyshev polynomials, which serve as a basis for the numerical approximation. The constructed scheme is subjected toarigorousstabilityandconvergenceanalysis,demonstratingitsreliabilityandsuitabilityfortheclassofproblemsunder consideration. To evaluate the methods effectiveness, numerical experiments were conducted on selected benchmark problems from the literature. The results highlight the efficiency and accuracy of the proposed approach, showing improved numerical performance compared to existing methods. The hybrid continuous formulation ensures better approximation properties while maintaining computational efficiency. The stability properties confirm that the method remains robust across a range of problem scenarios, making it a viable tool for solving second-order differential equations. The study contributes to the ongoing advancement of numerical techniques for differential equations, particularly by leveraging hybrid continuous methods with polynomial-based approximations. The promising results from numerical experiments further establish the potential of this approach for broader applications in computational mathematics and applied sciences.

 This study presents the development and analysis of a class of hybrid continuous methods designed for solving second-order initial value problems in ordinary differential equations. The formulation of the method is based on the application of a class of orthogonal and Chebyshev polynomials, which serve as a basis for the numerical approximation. The constructed scheme is subjected toarigorousstabilityandconvergenceanalysis,demonstratingitsreliabilityandsuitabilityfortheclassofproblemsunder consideration. To evaluate the methods effectiveness, numerical experiments were conducted on selected benchmark problems from the literature. The results highlight the efficiency and accuracy of the proposed approach, showing improved numerical performance compared to existing methods. The hybrid continuous formulation ensures better approximation properties while maintaining computational efficiency. The stability properties confirm that the method remains robust across a range of problem scenarios, making it a viable tool for solving second-order differential equations. The study contributes to the ongoing advancement of numerical techniques for differential equations, particularly by leveraging hybrid continuous methods with polynomial-based approximations. The promising results from numerical experiments further establish the potential of this approach for broader applications in computational mathematics and applied sciences.

 This study presents the development and analysis of a class of hybrid continuous methods designed for solving second-order initial value problems in ordinary differential equations. The formulation of the method is based on the application of a class of orthogonal and Chebyshev polynomials, which serve as a basis for the numerical approximation. The constructed scheme is subjected toarigorousstabilityandconvergenceanalysis,demonstratingitsreliabilityandsuitabilityfortheclassofproblemsunder consideration. To evaluate the methods effectiveness, numerical experiments were conducted on selected benchmark problems from the literature. The results highlight the efficiency and accuracy of the proposed approach, showing improved numerical performance compared to existing methods. The hybrid continuous formulation ensures better approximation properties while maintaining computational efficiency. The stability properties confirm that the method remains robust across a range of problem scenarios, making it a viable tool for solving second-order differential equations. The study contributes to the ongoing advancement of numerical techniques for differential equations, particularly by leveraging hybrid continuous methods with polynomial-based approximations. The promising results from numerical experiments further establish the potential of this approach for broader applications in computational mathematics and applied sciences.

 This study presents the development and analysis of a class of hybrid continuous methods designed for solving second-order initial value problems in ordinary differential equations. The formulation of the method is based on the application of a class of orthogonal and Chebyshev polynomials, which serve as a basis for the numerical approximation. The constructed scheme is subjected toarigorousstabilityandconvergenceanalysis,demonstratingitsreliabilityandsuitabilityfortheclassofproblemsunder consideration. To evaluate the methods effectiveness, numerical experiments were conducted on selected benchmark problems from the literature. The results highlight the efficiency and accuracy of the proposed approach, showing improved numerical performance compared to existing methods. The hybrid continuous formulation ensures better approximation properties while maintaining computational efficiency. The stability properties confirm that the method remains robust across a range of problem scenarios, making it a viable tool for solving second-order differential equations. The study contributes to the ongoing advancement of numerical techniques for differential equations, particularly by leveraging hybrid continuous methods with polynomial-based approximations. The promising results from numerical experiments further establish the potential of this approach for broader applications in computational mathematics and applied sciences.

Makale detayları

Hybrid continuous multi-step method for second order problems in ordinary differential equations

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355935

pISSN:

2980-3020

Block Method

Hybrid method

Initial Value Problems

One-fourth Step Order

Interpolation and Collocation

Sayı

Makale detayları

Hybrid continuous multi-step method for second order problems in ordinary differential equations

Yazarlar: N.A.

Yayıncı: Istanbul University

Ana Başlıklar: Pure Mathematics (Other)

Dergi: Istanbul Journal of Mathematics Vol.3 Issue 1, pp.1-11

Belge Tipi: Makale

Yayın Tarihi: 6/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001355935

pISSN: 2980-3020

Block Method

Hybrid method

Initial Value Problems

One-fourth Step Order

Interpolation and Collocation

Sayı

Yazarlar:

N.A.

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.1-11

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355935

pISSN:

2980-3020