SeMA https://doi.org/10.1007/s40324-018-0161-5 Improved variational iteration method for solving a class of nonlinear Fredholm integral equations M. H. Daliri 1 · J. Saberi-Nadjafi 1 Received: 1 December 2017 / Accepted: 3 May 2018 © Sociedad Española de Matemática Aplicada 2018 Abstract In this paper, an efficient numerical method which is a combination of the varia- tional iteration method and the spectral collocation method is developed for solving a class of nonlinear Fredholm integral equations (NFIEs). This method is easy to implement, requir- ing no tedious computational work and possesses the spectral accuracy. In addition, it does not require calculating Adomian’s polynomials and Lagrange’s multiplier values. Several numerical examples are included to demonstrate the validity and efficiency of the proposed method. The obtained results have been compared with the exact solutions so that the high accuracy of the results are clear. Keywords Variational iteration method · Spectral collocation method · Nonlinear Fredholm integral equation Mathematics Subject Classification 45G10 · 45B05 · 65M70 1 Introduction Integral equations play a crucial role in many branches of science and engineering such as biological models, mathematical economics, continuum mechanics, potential theory, geophysics, electricity and magnetism, fluid dynamics, antenna synthesis problem commu- nication theory, radiation, etc. [4, 32, 33]. Analytical solutions of integral equations, either do not exist or it’s hard to compute. Eventual an exact solution is computable, the required calculations may be tedious, or the resulting solution may be difficult to interpret. Due to this, it is required to obtain an efficient numerical solution. There are numerous studies B J. Saberi-Nadjafi najafi141@gmail.com M. H. Daliri ho_daliri@yahoo.com 1 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran 123