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Meeting Minutes

Feb. 10

• Paper submitted to J. Sci. Comput. and arXiv.

Feb. 6

To Do:

• [X] Simplify the accuracy proof.
• [X] Add comments about numerical results obtained by using Calvo’s methods.
• [X] Abhijit: submit paper to J. Sci. Comput. and arxiv.

Feb. 2

• Using Calvo’s directional projection formulation gives similar results to relaxation
• fsolve doesn’t like solving underdetermined systems. We decided to leave this (using extra embedded methods) to future work.

To Do:

• [X] Try underdetermined system (use extra methods)
• [X] Try Calvo reformulation with normalized vectors
• [x] David: finish revising

Jan. 30

• Using different 1st-order embedded methods is sometimes better, sometimes worse
• Review key differences between Calvo’s approach and ours
• Some ideas that might be useful:
  • Normalize the increment vectors before solving for \(\gamma\)
  • Use extra embedded methods so we have an underdetermined system

Jan. 26

• Why do the two 3rd-order methods behave so differently?
• Convergence test using 1st-order embedded method (KdV 1-soliton)
• If it works, try a true embedded 1st-order method (e.g., set \(b_i=1/s\) for all \(i\))
• Find discussion of using 1st-order embedded methods in literature (David)