Abstract
Three methods to solve two classes of integral equations of the second kind are introduced in this paper. Firstly, two Kantorovich methods are proposed and examined to numerically solving an integral equation appearing from mathematical modeling in biology. We use a sequence of orthogonal nite rank projections. The rst method is based on general grid projections. The second one is established by using the shifted Legendre polynomials. We establish a new convergence analysis and we prove the associated theorems. Secondly, a new Nystrom method is introduced for solving Fredholm integral equation of the second kind.
Highlights
In this paper, we introduce three methods to solve two classes of integral equations of the second kind
We introduce a new Nystrom method for solving the integral equation (3.1)
Equation (3.3) reads as n ν=1 ων θν cos 2[(n + 1)/2]θν 1)/2] + 1) sin(θν + θc) sin(θν θc)
Summary
T x, en,j en,j . Applying T to both sides of equation (2.3), and performing the inner product with en,i to both sides of this equation, we get n T en,j, en,i = T f, en,i , or, equivalently, where and (In − An)Xn = bn, Xn(j) := T xn, en,j , An(i, j) := T en,j, en,i , Hence bn(i) := T f, en,i . 1 0 f (τ )k(τ − s) ds.
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