This lesson covers the application of the Galerkin method, least square method, and collocation method in solving differential equations. It explains the process of reducing the strong form of governing differential equations to the weak form using the weighted residual statement. The lesson also discusses the benefits of using the weak form, such as a wider choice of trial functions due to reduced order of continuity requirements. It further elaborates on how natural boundary conditions are automatically incorporated during the reduction process. The lesson concludes with a comparison of the strong form solution and weak form solution, highlighting the restrictions of choosing the trial function in the weak form solution.

- The Galerkin method, least square method, and collocation method are effective in solving differential equations.
- The weak form of governing differential equations offers a wider choice of trial functions due to reduced order of continuity requirements.
- Natural boundary conditions are automatically incorporated during the reduction process from strong form to weak form.
- The weak form solution can be more accurate than the strong form solution.
- There are restrictions on choosing the trial function in the weak form solution.

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