# psbanerjee/numerical-analysis architecture

> Architecture diagram of the GitHub repository psbanerjee/numerical-analysis, generated by GitDiagram from its file tree, README and a sample of source files (last updated 2026-09-27). It is an AI-made overview: check details against the source.

- Interactive diagram: https://gitdiagram.com/psbanerjee/numerical-analysis
- Repository: https://github.com/psbanerjee/numerical-analysis

## Overview

This repository is a collection of numerical-analysis examples: a user runs a script or notebook to apply a method to a numerical problem. The README documents root finding, ODE solving, numerical integration, two finite-difference applications, and Monte Carlo estimation. The sampled Python source confirms the Newton–Raphson example iterates toward a root and prints it. Notebook contents were not sampled, so their internal call flow is not shown.

Main entry points: [`Root Finding.ipynb`](https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding.ipynb) (Root Methods), [`Root Finding Using Newton Raphson Method.py`](https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding%20Using%20Newton%20Raphson%20Method.py) (Newton–Raphson), [`Ordinary Differential Equation.ipynb`](https://github.com/psbanerjee/numerical-analysis/blob/main/Ordinary%20Differential%20Equation.ipynb) (ODE Methods), [`Numerical Integration.ipynb`](https://github.com/psbanerjee/numerical-analysis/blob/main/Numerical%20Integration.ipynb) (Integration Methods)

## Diagram (Mermaid)

```mermaid
flowchart TD

subgraph group_roots["Root Finding"]
  node_root_notebook["Root Methods<br/>[Root Finding.ipynb]"]
  node_newton_script["Newton–Raphson"]
end

subgraph group_odes["ODE Solving"]
  node_ode_notebook["ODE Methods"]
end

subgraph group_integration["Integration"]
  node_integration_notebook["Integration Methods"]
end

subgraph group_finite_difference["Finite Difference"]
  node_tise_notebook["TISE Solver"]
  node_heat_notebook["Heat Equation"]
end

subgraph group_monte_carlo["Monte Carlo"]
  node_monte_carlo_notebook["Pi Estimation<br/>[Monte Carlo.ipynb]"]
end

node_user(("User"))

node_user -->|"runs"| node_root_notebook
node_user -->|"runs"| node_newton_script
node_user -->|"runs"| node_ode_notebook
node_user -->|"runs"| node_integration_notebook
node_user -->|"runs"| node_tise_notebook
node_user -->|"runs"| node_heat_notebook
node_user -->|"runs"| node_monte_carlo_notebook

click node_root_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding.ipynb"
click node_newton_script "https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding%20Using%20Newton%20Raphson%20Method.py"
click node_ode_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Ordinary%20Differential%20Equation.ipynb"
click node_integration_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Numerical%20Integration.ipynb"
click node_tise_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Finite%20Difference%20Method.ipynb"
click node_heat_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Heat%20Equation%20using%20Finite%20Difference%20Method.ipynb"
click node_monte_carlo_notebook "https://github.com/psbanerjee/numerical-analysis/blob/main/Monte%20Carlo.ipynb"

classDef toneNeutral fill:#f8fafc,stroke:#334155,stroke-width:1.5px,color:#0f172a
classDef toneBlue fill:#dbeafe,stroke:#2563eb,stroke-width:1.5px,color:#172554
classDef toneAmber fill:#fef3c7,stroke:#d97706,stroke-width:1.5px,color:#78350f
classDef toneMint fill:#dcfce7,stroke:#16a34a,stroke-width:1.5px,color:#14532d
classDef toneRose fill:#ffe4e6,stroke:#e11d48,stroke-width:1.5px,color:#881337
classDef toneIndigo fill:#e0e7ff,stroke:#4f46e5,stroke-width:1.5px,color:#312e81
classDef toneTeal fill:#ccfbf1,stroke:#0f766e,stroke-width:1.5px,color:#134e4a
class node_root_notebook,node_newton_script,node_user toneBlue
class node_ode_notebook toneAmber
class node_integration_notebook toneMint
class node_tise_notebook,node_heat_notebook toneRose
class node_monte_carlo_notebook toneIndigo
```

## Components

### Root Finding

- [Root Methods](https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding.ipynb): `Root Finding.ipynb`
- [Newton–Raphson](https://github.com/psbanerjee/numerical-analysis/blob/main/Root%20Finding%20Using%20Newton%20Raphson%20Method.py): `Root Finding Using Newton Raphson Method.py`

### ODE Solving

- [ODE Methods](https://github.com/psbanerjee/numerical-analysis/blob/main/Ordinary%20Differential%20Equation.ipynb): `Ordinary Differential Equation.ipynb`

### Integration

- [Integration Methods](https://github.com/psbanerjee/numerical-analysis/blob/main/Numerical%20Integration.ipynb): `Numerical Integration.ipynb`

### Finite Difference

- [TISE Solver](https://github.com/psbanerjee/numerical-analysis/blob/main/Finite%20Difference%20Method.ipynb): `Finite Difference Method.ipynb`
- [Heat Equation](https://github.com/psbanerjee/numerical-analysis/blob/main/Heat%20Equation%20using%20Finite%20Difference%20Method.ipynb): `Heat Equation using Finite Difference Method.ipynb`

### Monte Carlo

- [Pi Estimation](https://github.com/psbanerjee/numerical-analysis/blob/main/Monte%20Carlo.ipynb): `Monte Carlo.ipynb`

### Other components

- **User**

## Connections

- User → Root Methods: runs
- User → Newton–Raphson: runs
- User → ODE Methods: runs
- User → Integration Methods: runs
- User → TISE Solver: runs
- User → Heat Equation: runs
- User → Pi Estimation: runs