Numerical solution for solving special eighth- order linear boundary value problems using Legendre Galerkin method

In this paper, Galerkin method has been introduced using Legendre polynomials as basis functions over the interval ½1; 1 to solve the eighth-order linear boundary value problems with two-point boundary conditions. LegendreGalerkinmethod is an effective tool in numerically solving such problems. The performance and applicability of the method is illustrated through some examples that reveal the method presents much better results. The obtained numerical results are convincing and very close to the analytical ones