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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does FDM stand for?
π‘ Hint: Remember the focus on how we approximate derivatives.
Question 2
Easy
What is the main advantage of using FEM?
π‘ Hint: Think about problems with uneven shapes.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What do PDEs model?
- Single physical phenomena
- Multidimensional physical phenomena
- Only abstract concepts
π‘ Hint: Consider the context of heat and fluid dynamics.
Question 2
True or False: FDM is effective for complex geometries.
- True
- False
π‘ Hint: Remember the limitations discussed on geometries.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the following heat equation using FDM: βu/βt = Ξ±βΒ²u/βxΒ² with u(0,t)=0, u(L,t)=0, and initial condition u(x,0)=f(x). Outline your approach carefully.
π‘ Hint: Think about how the boundary conditions affect your grid.
Question 2
Using FEM, reformulate the Poisson equation -dΒ²u/dxΒ² = f(x) into its weak form, and describe the steps to set up the global system of equations.
π‘ Hint: Remember integration by parts reduces derivatives in the equation.
Challenge and get performance evaluation