A combined efficient method for approximate two-dimensional integral equations

Document Type : Full Length Article

Authors

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Abstract

In this paper, we combine the two-dimensional (2D) Haar wavelet functions (HWFs) with the block-pulse functions (BPFs) to solve the 2D linear
Volterra-Fredholm integral equations (2D-L(VF)IE), so we present a new hybrid computational effcient method based on the 2D-HWFs and 2D-BPFs to approximate the solution of
the 2D linear Volterra-Fredholm integral equations. In fact, the HWFs and their
relations to the BPFs are employed to derive a general procedure to form
operational matrix of Haar wavelets. Theoretical error
analysis of the proposed method is done. Finally some examples are
presented to show the effectiveness of the proposed method.

Graphical Abstract

A combined efficient method for approximate two-dimensional integral equations

Keywords

Main Subjects


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Volume 9, Issue 4
December 2024
Pages 269-287
  • Receive Date: 18 October 2024
  • Revise Date: 07 November 2024
  • Accept Date: 23 November 2024
  • Publish Date: 01 December 2024