Application of the homotopy perturbation method for weakly singular Volterra integral equations

Ahmet Altürk

Makale detayları

Application of the homotopy perturbation method for weakly singular Volterra integral equations

Yazarlar:

Ahmet Altürk

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.13 Issue 3, pp.201-213

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338161

pISSN:

1304-7981

Anahtar kelimeler:

Özet:

 In this paper, we study a weakly singular Volterra integral equation of the second kind with the kernel displaystyle Kx,t  left fractxright nufrac1t, for some nu 0 and xin0,X. The powerful homotopy perturbation method HPM is initially applied to find a solution to the integral equation for nu  1. We then consider the interesting case where 0 nu  1. Applying the homotopy perturbation method constructed by a convex homotopy or other series-related methods produces unwanted results for this case. In this study, we propose conditions to be imposed to overcome this issue. In addition, for completeness, we investigate all cases where nuin mathbbR. Some numerical examples are provided to confirm the simplicity and applicability of the applied methods.

 In this paper, we study a weakly singular Volterra integral equation of the second kind with the kernel displaystyle Kx,t  left fractxright nufrac1t, for some nu 0 and xin0,X. The powerful homotopy perturbation method HPM is initially applied to find a solution to the integral equation for nu  1. We then consider the interesting case where 0 nu  1. Applying the homotopy perturbation method constructed by a convex homotopy or other series-related methods produces unwanted results for this case. In this study, we propose conditions to be imposed to overcome this issue. In addition, for completeness, we investigate all cases where nuin mathbbR. Some numerical examples are provided to confirm the simplicity and applicability of the applied methods.

 In this paper, we study a weakly singular Volterra integral equation of the second kind with the kernel displaystyle Kx,t  left fractxright nufrac1t, for some nu 0 and xin0,X. The powerful homotopy perturbation method HPM is initially applied to find a solution to the integral equation for nu  1. We then consider the interesting case where 0 nu  1. Applying the homotopy perturbation method constructed by a convex homotopy or other series-related methods produces unwanted results for this case. In this study, we propose conditions to be imposed to overcome this issue. In addition, for completeness, we investigate all cases where nuin mathbbR. Some numerical examples are provided to confirm the simplicity and applicability of the applied methods.

 In this paper, we study a weakly singular Volterra integral equation of the second kind with the kernel displaystyle Kx,t  left fractxright nufrac1t, for some nu 0 and xin0,X. The powerful homotopy perturbation method HPM is initially applied to find a solution to the integral equation for nu  1. We then consider the interesting case where 0 nu  1. Applying the homotopy perturbation method constructed by a convex homotopy or other series-related methods produces unwanted results for this case. In this study, we propose conditions to be imposed to overcome this issue. In addition, for completeness, we investigate all cases where nuin mathbbR. Some numerical examples are provided to confirm the simplicity and applicability of the applied methods.

Makale detayları

Application of the homotopy perturbation method for weakly singular Volterra integral equations

Yazarlar:

Ahmet Altürk

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.13 Issue 3, pp.201-213

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338161

pISSN:

1304-7981

Volterra integral equations

Homotopy perturbation method

Weakly singular kernel

Perturbation

Sayı

Makale detayları

Application of the homotopy perturbation method for weakly singular Volterra integral equations

Yazarlar: Ahmet Altürk

Yayıncı: Tokat Gaziosmanpasa University

Ana Başlıklar: Mathematical Methods and Special Functions

Dergi: Journal of New Results in Science Vol.13 Issue 3, pp.201-213

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001338161

pISSN: 1304-7981

Volterra integral equations

Homotopy perturbation method

Weakly singular kernel

Perturbation

Sayı

Yazarlar:

Ahmet Altürk

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Mathematical Methods and Special Functions

Dergi:

Journal of New Results in Science Vol.13 Issue 3, pp.201-213

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338161

pISSN:

1304-7981