This is a Case Study in Scientific Computing on the Numerical Solution of an Electrochemical Cell Model using Analytical Approaches, Finite Differences and a Spectral Method. A group project submitted as part of the MSc in MMSC (Mathematical Modelling and Scientific Computing).
In the report, we will introduce necessary mathematical background on Laplace transforms and Chebyshev polynomials (Section 2), obtain an analytical solution using a similarity solution and Laplace-transform approach in Section 3, discuss the finite difference scheme one can use to solve the problem numerically in Section 4 and finally introduce the Chebyshev spectral method used for most results in this report (Section 5).
The Python code can be found in Full_Solution.py.
The MatLab "code" for the numerical solution of the 1d and 2d cases is located in Matlab.
To compile the spectral solver, please run
mkdir build/
conan install . --output-folder=build --build=missing
cd build/
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j4
cd ../and then run either ./build/main for the GUI or ./build/generatePlots to reproduce the spectral results (located in results along with other diagrams).