Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations

• A new operational matrix for integration of Bernoulli polynomials is introduced.
• A collocation method is used to reduce equations to systems of algebraic equations.
• Some error bounds and convergence results are provided for the proposed method.
• The efficiency and applicability of the technique are checked by some examples.

A new operational matrix for integration of Bernoulli polynomials is introduced. By using this new operational matrix of integration and the so-called collocation method, linear Volterra and nonlinear Volterra–Fredholm–Hammerstein integral equations are reduced to systems of algebraic equations with unknown Bernoulli coefficients. Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the technique.