Finite Element Method with Applications in Engineering

2.5 FURTHER NUMERICAL EXAMPLES

Example 2.5

Solve the differential equation ɸ″ - ɸ = x² with boundary conditions ɸ(x = 0) = 0 and ɸ(x = 1) = 0, by Point Collation, Least Square, Galerkin and Rayleigh–Ritz Method and compare results with the exact solution.

Solution:

1. Point CollocationSolution that satisfies boundary conditions is

    

   

    

   Limiting it to two terms,

    

   

    

   Then

    

   

    

   and

    

    

   Substituting values of in original equation, error ε is ...