20.2.1 - Finite Difference Method (FDM)
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Practice Questions
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What does FDM stand for?
💡 Hint: Think about how we approximate derivatives.
Name a common application of FDM.
💡 Hint: Consider phenomena modeled by PDEs.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the acronym FDM stand for?
💡 Hint: Think of how we approximate derivatives.
True or False: The explicit method in FDM is unconditionally stable.
💡 Hint: Recall the conditions for stability in explicit methods.
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Challenge Problems
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Using FDM, solve the 1D heat equation with boundary conditions u(0,t)=0 and u(L,t)=100 over a domain of length L=10 with appropriate discretization.
💡 Hint: Draw out the grid and apply the finite difference formulas.
Propose a method to overcome the stability issues of explicit methods when implementing FDM. Discuss the advantages and potential limitations.
💡 Hint: Consider stability versus computational cost when discussing methods.
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