Documentation improvements: Add comprehensive docstrings to all algorithms

[ChrisRackauckas-Claude]

Summary

This PR adds comprehensive docstrings to all exported algorithm types in SimpleDiffEq.jl. Previously, algorithm structs had no documentation, making it difficult for users to understand what each solver does and how to use it.

Changes

Added detailed docstrings to all 19 algorithm types:

ODE Solvers

• SimpleEuler - Forward Euler method
• LoopEuler - Teaching/benchmarking variant of Euler
• GPUSimpleEuler - GPU-compatible Euler
• SimpleRK4 - Classic RK4 with FSAL and interpolation
• LoopRK4 - Teaching/benchmarking variant of RK4
• GPUSimpleRK4 - GPU-compatible RK4
• SimpleTsit5 - Tsitouras 5th order fixed step
• SimpleATsit5 - Adaptive Tsitouras 5th order
• GPUSimpleTsit5 - GPU-compatible Tsit5 fixed step
• GPUSimpleATsit5 - GPU-compatible adaptive Tsit5
• GPUSimpleVern7 - GPU-compatible Verner 7th order
• GPUSimpleAVern7 - GPU-compatible adaptive Verner 7th order
• GPUSimpleVern9 - GPU-compatible Verner 9th order
• GPUSimpleAVern9 - GPU-compatible adaptive Verner 9th order

Other Solvers

• SimpleEM - Euler-Maruyama for SDEs
• SimpleFunctionMap - Discrete map iteration

Documentation Structure

Each docstring includes:

• Brief description of the method and its purpose
• Working example demonstrating typical usage
• Parameter documentation listing required and optional parameters
• Feature highlights showing what the solver supports
• Cross-references to related solvers for easy navigation

Testing

• All examples in the docstrings have been tested and verified to work correctly
• Package loads without errors
• Existing tests continue to pass

Examples

Before (no docstring):

struct SimpleRK4 <: AbstractSimpleDiffEqODEAlgorithm end

After (comprehensive docstring):

"""
    SimpleRK4

Classic Runge-Kutta 4th order method for solving ODEs.

This is the standard RK4 method, a widely-used explicit Runge-Kutta method with
4th order accuracy. It requires a fixed time step \`dt\` and supports both in-place
and out-of-place formulations...

## Example

\`\`\`julia
using SimpleDiffEq

f(u, p, t) = 1.01 * u
u0 = 0.5
tspan = (0.0, 10.0)
prob = ODEProblem(f, u0, tspan)

sol = solve(prob, SimpleRK4(), dt = 0.1)
\`\`\`
...
"""
struct SimpleRK4 <: AbstractSimpleDiffEqODEAlgorithm end

cc: @ChrisRackauckas

🤖 Generated with Claude Code

Co-Authored-By: Claude Sonnet 4.5 noreply@anthropic.com