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.
Fallahpour, M., Ezzati, R., & Hashemizadeh, E. (2024). A combined efficient method for approximate two-dimensional integral equations. Journal of Discrete Mathematics and Its Applications, 9(4), 269-287. doi: 10.22061/jdma.2024.11175.1088
MLA
Mohsen Fallahpour; Reza Ezzati; Elham Hashemizadeh. "A combined efficient method for approximate two-dimensional integral equations", Journal of Discrete Mathematics and Its Applications, 9, 4, 2024, 269-287. doi: 10.22061/jdma.2024.11175.1088
HARVARD
Fallahpour, M., Ezzati, R., Hashemizadeh, E. (2024). 'A combined efficient method for approximate two-dimensional integral equations', Journal of Discrete Mathematics and Its Applications, 9(4), pp. 269-287. doi: 10.22061/jdma.2024.11175.1088
VANCOUVER
Fallahpour, M., Ezzati, R., Hashemizadeh, E. A combined efficient method for approximate two-dimensional integral equations. Journal of Discrete Mathematics and Its Applications, 2024; 9(4): 269-287. doi: 10.22061/jdma.2024.11175.1088
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