Abstract
A novel numerical method is developed for solving two-dimensional linear Fredholm integral equations of the second kind by integral mean value theorem. In the proposed algorithm, each element of the generated discrete matrix is not required to calculate integrals, and the approximate integral operator is convergent according to collectively compact theory. Convergence and error analyses of the approximate solution are provided. In addition, an algorithm is given. The reliability and efficiency of the proposed method will be illustrated by comparison with some numerical results.
Highlights
This paper proposes a novel numerical method based on integral mean value theorem (IMVT) for solving twodimensional linear Fredholm integral equations (FIE) of the second kind
The linear integral equation is considered as u − Ku = f, (1)
This paper introduces a new method by changing FIE to systems of linear algebraic equations through IMVT
Summary
This paper proposes a novel numerical method based on integral mean value theorem (IMVT) for solving twodimensional linear Fredholm integral equations (FIE) of the second kind. In [16], researchers presented some orthogonal polynomials as Galerkin method’s basis functions to solve the linear FIE of the second kind. Both of the collocation method and Galerkin method belong to the projection method, and the key is to come up with good basis functions. Integral mean value method was proposed for one-dimensional integrals [7] and multiple integrals [18] They transform integral equations to nonlinear systems of equations without any basis functions.
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