Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics

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Numerical Algorithm for Two-dimensional Volterra-Fredholm Integral Equations and Its Convergence Analysis

XIE Jiaquan1,2,   LIU Xiaoqi1,   ZHANG Jiale1   

  1. 1. Department of Mathematics, Taiyuan Normal University, Jinzhong 030619;
    2. Key Laboratory for Engineering & Computational Science, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong 030619
  • Online:2022-12-15 Published:2022-12-15
  • Supported by:
    The National Natural Science Foundation of China (52005360); the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (2021L403).

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Abstract: A two-dimensional nonlinear Volterra-Fredholm Hammerstein integral equation is numerically solved by using the two-dimensional block pulse function as the basis function. Firstly, the definition of the block pulse function and the vector representation of the basis function are introduced. Secondly, according to the disjointness and orthogonality of

two-dimensional block pulse functions, the integral operator matrix and product operator matrix of the basis vector are derived. Thirdly, the operator matrix is used to transform the problem to be solved into the product form of a series of vectors, and the unknown variables are discretized by the collocation method to obtain the numerical solution of the original problem, Finally, the feasibility and convergence of the proposed algorithm are verified by two numerical examples.

Key words: Volterra-Fredholm integral equations, two-dimensional Block-Pulse functions, ope-rational matrix, numerical solutions, convergence

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