5 - Numerical Solutions of Partial Differential Equations
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Practice Questions
Test your understanding with targeted questions
What does FDM stand for?
💡 Hint: Remember the focus on how we approximate derivatives.
What is the main advantage of using FEM?
💡 Hint: Think about problems with uneven shapes.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What do PDEs model?
💡 Hint: Consider the context of heat and fluid dynamics.
True or False: FDM is effective for complex geometries.
💡 Hint: Remember the limitations discussed on geometries.
2 more questions available
Challenge Problems
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Solve the following heat equation using FDM: ∂u/∂t = α∂²u/∂x² with u(0,t)=0, u(L,t)=0, and initial condition u(x,0)=f(x). Outline your approach carefully.
💡 Hint: Think about how the boundary conditions affect your grid.
Using FEM, reformulate the Poisson equation -d²u/dx² = f(x) into its weak form, and describe the steps to set up the global system of equations.
💡 Hint: Remember integration by parts reduces derivatives in the equation.
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