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

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：65R20,Linear Volterra integral equations,Nonlinear Volterra–Fredholm–Hammerstein integral equations,Bernoulli polynomials,Operational matrix,Collocation method

论文评审过程：Received 31 December 2013, Revised 4 June 2014, Available online 12 August 2014.

论文官网地址：https://doi.org/10.1016/j.cam.2014.07.018