Notebooks/PaperFigures.ipynb

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   "source": [
    "### Part I: Finite-Difference Discretization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b021c225",
   "metadata": {},
   "source": [
    "1. [Error analysis](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Error%20Analysis%20(FD).ipynb) —— Performs error analysis on the finite-difference discretization."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "713d43ee",
   "metadata": {},
   "source": [
    "### Part II: Spectral Discretization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d0dc6a8",
   "metadata": {},
   "source": [
    "1. [Error analysis](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Error%20Analysis%20(Spectral).ipynb) —— Performs error analysis on the spectral discretization."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2396614",
   "metadata": {},
   "source": [
    "### Part III: Additional Numerical Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1710bf8",
   "metadata": {},
   "source": [
    "1. [Absolute stability region along with eigenvalues](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Absolute%20stability%20region%20with%20eigenvalues.ipynb) —— Plots of the absolute stability regions along with eigenvalues. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf74f463",
   "metadata": {},
   "source": [
    "2. [Comparison with large random matrices](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Comparison%20with%20large%20random%20matrices.ipynb) —— Compares the pdf generated by our algorithm with the largest eigenvalue of certain large random matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d3b417",
   "metadata": {},
   "source": [
    "3. [Evolution of the solution](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Evolution%20of%20the%20solution.ipynb) —— Waterfall plots of the density of the solution and contour plots of the solution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "604b5fdb",
   "metadata": {},
   "source": [
    "4. [Density of the Tracy-Widom distribution](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Density%20of%20the%20TW%20distribution.ipynb) —— Waterfall plot of the density of the Tracy-Widom distribution along with a two-dimensional version."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0b4a86b",
   "metadata": {},
   "source": [
    "5. [Limiting densities of the other eigenvalues](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Limiting%20densities%20of%20other%20eigenvalues.ipynb) —— Densities of the other eigenvalues."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b58b4c3",
   "metadata": {},
   "source": [
    "### Part IV: Appendices"
   ]
  },
  {
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   "id": "b7041ca8",
   "metadata": {},
   "source": [
    "1. [BDF3](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/BDF3.ipynb) —— The gap of $\\Delta x$ causing instability for BDF3."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b09dc1e2",
   "metadata": {},
   "source": [
    "2. [BDF4](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/BDF4.ipynb) —— The gap of $\\Delta x$ causing instability for BDF4."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb6e628e",
   "metadata": {},
   "source": [
    "3. [BDF5](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/BDF5.ipynb) —— The gap of $\\Delta x$ causing instability for BDF5."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f25120f",
   "metadata": {},
   "source": [
    "4. [BDF6](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/BDF6.ipynb) —— The gap of $\\Delta x$ causing instability for BDF6."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aedeb947",
   "metadata": {},
   "source": [
    "5. [The case when $\\beta=\\infty$](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/The%20case%20when%20%CE%B2%3DInf.ipynb) —— Contour plot of the solution with respect to $x$ and $\\theta$ when $\\beta=\\infty$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f57ef49",
   "metadata": {},
   "source": [
    "6. [Spectral discretization with DIRK methods](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Spectral%20discretization%20with%20DIRK%20methods.ipynb) —— Applying some DIRK methods on the spectral discretization."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b3468d2",
   "metadata": {},
   "source": [
    "7. [Spectral discretization with adaptive time stepping methods](https://github.com/Yiting687691/TracyWidomBeta.jl/blob/main/Notebooks/Spectral%20discretization%20with%20adaptive%20time%20stepping%20methods.ipynb) —— Applying some adaptive time stepping methods on the spectral discretization."
   ]
  }
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