Damping of Crank-Nicolson error oscillations

Area of Science:

• Computational electrochemistry
• Numerical methods for differential equations

Background:

• The Crank-Nicolson method is widely used for simulations but suffers from oscillations.
• These oscillations can hinder the accuracy and reliability of electrochemical computations.

Purpose of the Study:

• To investigate methods for damping oscillations in Crank-Nicolson simulations.
• To evaluate the effectiveness of different damping techniques in electrochemical systems.

Main Methods:

• Applied subdivision of the first time interval (Pearson method).
• Utilized exponentially increasing subintervals.
• Incorporated a backward implicit (BI) step at the beginning of the simulation.

Main Results:

• Pearson method and exponentially increasing subintervals effectively damped oscillations in 1D systems.
• A single backward implicit step was highly effective for 2D electrochemical microdisk simulations.
• Subdivision of the first time interval was computationally less expensive than expanding intervals over the entire simulation period.

Conclusions:

• The backward implicit step is recommended for 2D electrochemical microdisk simulations using Crank-Nicolson.
• Subdivision of the first time interval offers a computationally efficient alternative for damping oscillations.
• Optimizing expansion parameters is crucial for exponentially increasing subintervals, which can be computationally intensive.