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<p>In this paper, we used higher order Haar wavelet method (HOHWM), introduced by Majak et al. [1], for approximate solution of second order integro-differential equations (IDEs) of second-kind. It is improvement of long-established Haar wavelet collocation method (HWCM) which has been much popular among researchers and has many applications in literature. Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM, depending on parameter <i>λ</i> for values 1 and 2, respectively. Several problems available in the literature of both, Volterra and Fredholm type of IDEs, are tested and compared with HWCM to illustrate the performance of our proposed method.</p>

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Higher order Haar wavelet method for the numerical solution of second-order integro-differential equations

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Shumaila Yasmeen,
  • Rohul Amin

摘要

In this paper, we used higher order Haar wavelet method (HOHWM), introduced by Majak et al. [1], for approximate solution of second order integro-differential equations (IDEs) of second-kind. It is improvement of long-established Haar wavelet collocation method (HWCM) which has been much popular among researchers and has many applications in literature. Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM, depending on parameter λ for values 1 and 2, respectively. Several problems available in the literature of both, Volterra and Fredholm type of IDEs, are tested and compared with HWCM to illustrate the performance of our proposed method.