F-transform utility in the operational-matrix approach to the Volterra integral equation

被引：0

作者：

Perfilieva, Irina ^{[1
]}

Ziari, Shokrollah ^{[2
]}

Nuraei, Rahele ^{[2
]}

Pham, Thi Minh Tam ^{[3
]}

机构：

[1] Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, 30 Dubna 22, Ostrava 1, Czech Republic

[2] Islamic Azad Univ, Dept Math, South Tehran Branch, Tehran, Iran

[3] Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, Ostrava 70103, Czech Republic

来源：

FUZZY SETS AND SYSTEMS | 2024年 / 475卷

关键词：

Linear Volterra integral equation; Fuzzy transform; Operational matrix; Computational complexity; NUMERICAL-SOLUTION; COLLOCATION METHOD; FUZZY TRANSFORMS; 2ND KIND; FREDHOLM; COMPRESSION; APPROXIMATION; DECOMPRESSION;

D O I：

10.1016/j.fss.2023.108764

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The proposed approach, based on the F-transform, consists in constructing an operational matrix for the Volterra integral equation as a Hadamard product of two matrices, one of which refers to the Volterra operator, and the other to its kernel. As a result, the F-transformed form of the entire equation reduces to a system of linear equations with a triangular matrix. This makes the corresponding numerical method for solving the Volterra integral equation efficient and low computational. We provide all the necessary proofs of the supporting statements, including the convergence of the method, and estimate its computational complexity. Finally, we illustrate the proposed algorithm with test cases and compare their results with some recently published methods.

引用

页数：21

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