Abstract: In this paper we propose a new collocation method for
solving a mixed type Hammerstein equation. Following the idea of Kumar and
Sloan, the method is applied to approximate the solution not to the equation in
its original form, but rather to an equivalent system of equations Each of functions is approximated by a polynomial of degree n,
with coefficients determined by collocation at the Chebyshev-Gauss-Lobatto
nodes. Clenshaw-Curtis rules are applied to compute the integrals involved
numerically. A convergence result is established under suitable conditions.
Advantages of the proposed method, compared with existing methods in the
literature, are discussed. An illustrative example is included to show the
accuracy of the proposed method.
Keywords and phrases: spectral methods, Hammerstein integral equations of mixed type.
