Numerical approximation of a nonlinear fourth-order integro-differential equation by spectral method

摘要

A spectral method is developed to approximate a nonlinear fourth-order integro-differential equation. An iterative algorithm is proposed to solve the discrete algebraic system. Convergence analysis of the iteration is carried out. An error estimate is also derived for the proposed method. Several numerical examples are presented to confirm the efficiency and accuracy of the overall algorithm.