Numerical Simulations of Nonlinear Partial Differential Equations
| Method | Note | Implemented |
|---|---|---|
| Split-Step Fourier Method | Too noisy | ○ |
| Pseudo-spectral Method (Recommended) | A MATLAB implementation is in the DMD book (Kutz, et. al., 2016) | ○ |
| Method | Note | Implemented |
|---|---|---|
| Differential Method | 1st-order accurate in time | ○ |
| Crank-Nicolson Method (Recommended) | 2nd-order accurate in time | ○ |
Suarez, P. (2015), "An introduction to the Split Step Fourier Method using MATLAB," Unpublished. https://doi.org/10.13140/RG.2.1.1394.0965.
Wani, S. S., and Thakar, S. H. (2013), “Crank-Nicolson Type Method for Burgers Equation,” International Journal of Applied Physics and Mathematics, 324–328. https://doi.org/10.7763/IJAPM.2013.V3.230.