Numeric Methods ^v3

A modern cross-platform application for interactive and step-by-step exploration of numerical methods.

Translations: English | Русский | 简体中文 | O'zbekcha

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📥 Downloads

Numeric Methods targets three main environments from a single codebase: Web, Desktop (Windows / Linux), and Mobile (Android APK). All signed binary packages and releases are hosted directly on GitHub Releases.

📱 Android (APK)

Package	Architecture / Target	Download Link
Numeric Methods APK (ARM64) (Recommended)	Optimized for modern 64-bit Android smartphones and tablets (arm64-v8a). Smaller file size and best runtime performance.	⬇️ Download ARM64 APK
Numeric Methods APK (Universal)	Compatible with all Android CPU architectures (arm64-v8a, armeabi-v7a, x86, x86_64).	⬇️ Download Universal APK

💡 Latest Release Mirror: You can always find the newest APK releases at the GitHub Releases page.

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💻 Desktop (Windows & Linux)

Platform	Format	Download Link
Windows 10 / 11 (64-bit)	NSIS Setup (.exe)	⬇️ Download Windows Installer
Windows 10 / 11 (64-bit)	Windows Installer (.msi)	⬇️ Download Windows MSI
Linux (Ubuntu / Debian)	Debian package (.deb)	⬇️ Download Debian Package
Linux (Universal)	Portable AppImage (.AppImage)	⬇️ Download AppImage

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🌐 Web Version

Instant access without installation:

• Production Web App (v3): sonli-usullar.uz
• Archive Version (v2): v2.sonli-usullar.uz

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🧮 Implemented Numerical Methods

The application includes 10 fundamental computational algorithms divided into 5 academic categories:

1. Algebraic & Transcendental Equations

• Bisection Method (Interval Halving): Finding roots by iteratively halving an interval $[a, b]$ where $f(a) \cdot f(b) < 0$. Convergence rate: $O(\log_2(1/\varepsilon))$.
• Newton-Raphson Method: Tangent-based root finding with quadratic convergence: $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$.

2. Systems of Linear Equations

• Tridiagonal Matrix Algorithm (Thomas / Sweep Method): An efficient $O(n)$ elimination solver for tridiagonal systems $a_i x_{i-1} + b_i x_i + c_i x_{i+1} = d_i$.

3. Polynomial Interpolation

• Lagrange Interpolation: Constructs the unique lowest-degree polynomial passing through a given set of data points: $L_n(x) = \sum_{i=0}^n y_i \prod_{j \neq i} \frac{x - x_j}{x_i - x_j}$.
• Newton Divided Differences Interpolation: Step-by-step divided difference table construction and polynomial evaluation.

4. Numerical Quadrature (Definite Integrals)

• Rectangle (Midpoint) Rule: Approximation using left, right, and midpoint Riemann sums ($O(h)$ to $O(h^2)$).
• Trapezoidal Rule: Linear approximation over subintervals: $I \approx \frac{h}{2} [y_0 + 2\sum y_i + y_n]$ ($O(h^2)$).
• Simpson's 1/3 Rule (Parabolic): Higher-order quadratic spline quadrature ($O(h^4)$).

5. Ordinary Differential Equations (ODEs / Cauchy Initial Value Problem)

• Euler's Method: First-order explicit step solver: $y_{i+1} = y_i + h \cdot f(x_i, y_i)$.
• Runge-Kutta 4th Order (RK4): Classic fourth-order predictor-corrector solver with weighted sub-step slopes ($k_1, k_2, k_3, k_4$).

✨ Key Features Across All Solvers

• 📈 Dynamic Interactive Charts: Powered by Recharts and custom coordinate axes with zoom, inspection, and function traces.
• 📐 Instant Formula Typography: High-speed client-side math typesetting via KaTeX.
• 📋 Audit Tables & Intermediate Steps: Complete step-by-step arithmetic tables showing residuals, error bounds, and convergence.
• 💾 Export Options: One-click table copying, raw CSV export, and high-resolution PNG snapshot download with timestamps.
• 🌐 Trilingual Localization: Seamless switching between Uzbek, Russian, and English.
• 🌗 Light / Dark Mode: High-contrast technical theme with open-corner aesthetic.

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🛠 Tech Stack

• Framework: Next.js 16 (App Router, Turbopack, output: "export")
• UI Library: React 19
• Native Runtime: Tauri v2 (Rust shell for Desktop and Android)
• Styling: Tailwind CSS 4
• Math Engine: Math.js (Symbolic parsing & numerical evaluation)
• Typography: KaTeX
• Charts: Recharts
• Icons: Lucide React
• Package Manager: Bun (Strict requirement)

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🚀 Getting Started (Development)

Prerequisites

• Bun (v1.2 or later)
• Rust (Required only for building Tauri desktop or mobile apps)

1. Install Dependencies

bun install

2. Run Next.js Web Dev Server

bun dev

Open http://localhost:3000 in your browser.

3. Build Static Web Export

bun run build
bun start

The static export will be written to the out/ directory, which is shared between web deployments (Netlify, Vercel) and the Tauri frontend.

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💻 Building Desktop (Tauri)

After configuring the Rust toolchain and platform dependencies:

# Run desktop development with live reload
bun td

# Build production installers (.exe, .msi, .deb, .AppImage)
bun tb

Configuration resides in src-tauri/tauri.conf.json.

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📱 Building Android APK

Requirements:

• Java JDK 17+
• Android SDK & NDK (r26d recommended)
• Android target architectures for Rust:

  rustup target add aarch64-linux-android armv7-linux-androideabi x86_64-linux-android

Build Commands:

# Initialize Android project structure
bun run tauri:android:init

# Run in an Android emulator or connected device
bun run tauri:android:dev

# Build Universal signed APK (runs on all devices)
bun run tauri:android:build --apk

# Build Split per-ABI APKs (optimized ARM64 APK)
bun run tauri:android:build --apk --split-per-abi

Generated APKs are located in:
src-tauri/gen/android/app/build/outputs/apk/

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🔄 Automatic Updates (Auto-Updater)

• Desktop (Windows/Linux): Integrated with Tauri's native signed updater (minisign public key). Automatically checks latest.json on GitHub Releases and updates in the background.
• Android: Embedded updater detector notifies users whenever a newer APK is released and opens the direct download link in the system browser.

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🤝 Contributing

Contributions are welcome! Please read CONTRIBUTING.md for full instructions before submitting code.

• 🐛 Found a bug? Submit a Bug Report.
• 💡 Have a feature idea? Submit a Feature Request.
• 🧮 Want to add a new numerical method? Check out the New Method Proposal and step-by-step implementation guide in CONTRIBUTING.md.
• 📜 Please review our Code of Conduct for community standards.

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📄 License & Terms of Use

This project is licensed under a Custom Non-Commercial & Attribution License. See the full text in LICENSE.

Key Terms:

• Educational & Non-Commercial: The Software and its compiled packages (Web, Desktop, Android APK) may be used freely for learning and research, but CANNOT be sold, monetized, or used for commercial gain.
• Preserve Original Author & Brand: The project brand ("Numeric Methods" / "Sonli Usullar") and the original authorship credits to Jasurbek Haydarov (@hexjasur) must remain intact and cannot be altered or removed.
• Forks & Contributions: You are welcome to fork the project, develop enhancements, and add your own name alongside the original author in the contributors list.
• Redistribution: You may redistribute derivative works only under identical license and attribution terms.

Contact:

• Author: Jasurbek Haydarov (@hexjasur)
• Official Website: sonli-usullar.uz
• Telegram: @KanYonA
• Email: jasurhaydarovcode@gmail.com