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This bot is designed to solve differential equations of various orders using numerical methods such as Euler's Method, Improved Euler's Method, Runge-Kutta Method, and Dormand-Prince Method. It provides a Telegram interface for users to input equations and receive solutions.
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<palign="center"> <em> A powerful Telegram bot designed for solving differential equations using advanced numerical methods. </em> </p>
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## Features
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- Supports solving 1st and higher-order differential equations.
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- Multiple numerical methods available:
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- Euler's Method
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- Improved Euler's Method
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- Runge-Kutta Method
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- Dormand-Prince Method
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- Generates plots of solutions for better visualization.
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- Solution history tracking.
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- Multilingual support.
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- Configurable settings for numerical methods, rounding precision, and language.
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-**Equation Solving**
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Capable of solving first-order and higher-order ordinary differential equations (ODEs).
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The bot accepts user-defined equations and initial conditions, automatically parsing and preparing them for numerical analysis.
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-**Numerical Methods**
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Implements a range of well-established numerical methods to approximate solutions with varying degrees of accuracy and computational efficiency:
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- Euler's Method;
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- Midpoint Method;
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- Heun's Method;
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- Runge-Kutta Method;
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- Dormand-Prince Method.
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-**Visualization**
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Automatically generates clear and informative plots of the computed solutions.
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These visualizations help users interpret the behavior of differential systems over time.
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-**History Tracking**
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Maintains a record of previously solved equations and their corresponding results, enabling users to revisit and review past computations.
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-**Multilingual Support**
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Offers interaction in multiple languages, enhancing accessibility and usability for users from diverse linguistic backgrounds.
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-**Customizable Settings**
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Provides a flexible interface for tailoring computational and interaction parameters to user preferences:
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-**Numerical Method** – Choose from a list of supported methods (e.g., Euler, Runge-Kutta, Dormand-Prince).
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-**Precision Control** – Set the number of decimal places to which numerical results are rounded.
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-**Language Selection** – Choose the interface language for all commands and responses.
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-**Hints Toggle** – Enable or disable contextual tips and usage hints to streamline the interface.
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