Efficient Numerical Algorithm for the Solution of Eight Order Boundary Value Problems by Haar Wavelet Method

Rohul Amin, Kamal Shah, Qasem M. Al-Mdallal, Imran Khan, Muhammad Asif

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, the Haar technique is applied to both nonlinear and linear eight-order boundary value problems. The eight-order derivative in the boundary value problem is approximated using Haar functions in this technique and the integration process is used to obtain the expression of the lower order derivative and the approximate solution of the unknown function. For the verification of validation and convergence of the proposed technique, three linear and two nonlinear examples are taken from the literature. The results are also compared with other methods available in the literature. Maximum absolute and root mean square errors at various collocation and Gauss points are contrasted with the exact solution. The convergence rate is also measured, which is almost equivalent to 2, using different numbers of collocation points.

Original languageEnglish
Article number34
JournalInternational Journal of Applied and Computational Mathematics
Volume7
Issue number2
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Boundary value problems
  • Collocation method
  • Gauss elimination method
  • Haar wavelet

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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