2D Heat Equation

Analysis and numerical methods for 2D heat equation

Project Progress

Week 1

• Formulation of problem
• Fundamental solution on various conditions
• Spectral analysis of heat equation
• DFT and FFT realization

Week 2

• Rewite the deduction of funtamental solution by another approach
• Minor fix: use the proper Hilbert space to express periodic boundary condition
• 1D FDM
  • Euler explicit method
• Framework for algorithm analysis
  • Consistency
• Enriched details of eigenfunction method

Week 3

• Further study of fundatmental solution
• DFT and FFT realization
• 1D FDM
  • Euler implicit method, Leapfrog method
  • Crank-Nicolson method

Planned

• Draw animated gif of fundatmental solution with respect to time variable