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User Guide

This guide covers the normal workflow: define problem, configure parameters, solve, inspect and export results.

Main menu

Buttons:

  • Solve: general equation workflows (ODE, difference equations, PDE, vector ODE)
  • Function Transform: transform scalar functions
  • Complex Problems: plugin workflows with dedicated UI and visualizations
  • Information: in-app help panel
  • Configuration: edit .env values through UI
  • Quit: close application

Solve workflow

1. Choose equation type

In Solve, choose one of:

  • ODE
  • Difference equation
  • PDE
  • Vector ODE

You can use predefined equations (YAML catalog) or custom expressions.

2. Define equation

For custom expressions:

  • ODE notation: f[0], f[1], f[2], ...
  • Vector notation: f[i,k] (component i, derivative order k)
  • Difference notation: f[0] for current term, n as index

Typical safe math functions are available (sin, cos, exp, log, sqrt, etc.).

3. Configure numeric parameters

  • Domain bounds and sample points
  • Initial/boundary values
  • Solver method (ODE)
  • Statistics to compute
  • PDE visualization mode

4. Solve and inspect

Result dialog includes:

  • statistics and metadata
  • interactive plots/tabs
  • derivative/axis selection without re-solving
  • export options (CSV/JSON/figures and MP4 when applicable)

Function Transform workflow

In Function Transform:

  1. Provide f(x) expression and optional parameters.
  2. Select transform (Fourier, Laplace, Taylor, Hilbert, Z-transform).
  3. Switch between curve view and coefficient view.
  4. Export transformed data and plots.

Complex Problems workflow

Complex Problems opens a selector dialog with a left module list and a right details panel.

Each plugin has its own:

  • configuration UI
  • specialized solver
  • dedicated result dialog and diagnostics

Most plugin dialogs include a collapsed How to configure section with:

  • short equation summary
  • physical interpretation
  • parameter meaning
  • expected visualizations

UI notation uses Unicode math formatting where possible. When a Unicode subscript does not exist (for example theta/phi), the UI uses base_subscript style such as N_θ, N_φ.

For current modules and details, see Complex Problems Guide.

Exports

By default, solves generate output files under output/:

  • solution_*.csv
  • solution_*.json
  • solution_*.png (or selected format)

Animation-capable dialogs can also export MP4.

Configuration workflow

Use Configuration in the main menu to edit environment-backed settings.

Categories include:

  • UI look and behavior
  • plot style/fonts/animation
  • solver defaults and tolerances
  • logging and update checks

Saving from the dialog restarts the app so settings apply cleanly.

See Configuration Reference for full key details.