differential-equations/benches

Benchmarks

This directory contains performance benchmarks for the ODE solver library.

Running Benchmarks

To run all benchmarks:

cargo bench

To run a specific benchmark file:

cargo bench --bench bs3_vs_dp5
cargo bench --bench simple_1d
cargo bench --bench orbit

Benchmark Suites

bs3_vs_dp5.rs - BS3 vs DP5 Comparison

Comprehensive performance comparison between the Bogacki-Shampine 3(2) method (BS3) and Dormand-Prince 4(5) method (DP5).

Test Problems:

1. Exponential Decay - Simple 1D problem: y' = -0.5*y
2. Harmonic Oscillator - 2D conservative system: y'' + y = 0
3. Nonlinear Pendulum - Nonlinear 2D system with trigonometric terms
4. Orbital Mechanics - 6D system with gravitational dynamics
5. Interpolation - Performance of dense output interpolation
6. Tolerance Scaling - How methods perform across tolerance ranges (1e-3 to 1e-7)

Expected Results:

• BS3 should be faster for moderate tolerances (1e-3 to 1e-6) on simple problems
  • Lower overhead: 4 stages vs 7 stages for DP5
  • FSAL property: effective cost ~3 function evaluations per step
• DP5 should be faster for tight tolerances (< 1e-7)
  • Higher order allows larger steps
  • Better for problems requiring high accuracy
• Interpolation: DP5 has more sophisticated interpolation, may be faster/more accurate

simple_1d.rs - Simple 1D Problem

Basic benchmark for a simple 1D exponential decay problem using DP5.

orbit.rs - Orbital Mechanics

6D orbital mechanics problem using DP5.

Benchmark Results Interpretation

Criterion outputs timing statistics for each benchmark:

• Time: Mean execution time with confidence interval
• Outliers: Number of measurements significantly different from the mean
• Plots: Stored in target/criterion/ (if gnuplot is available)

Performance Comparison

When comparing BS3 vs DP5:

1. For moderate accuracy (tol ~ 1e-5):

   • BS3 typically uses ~1.5-2x the time per problem
   • But this can vary by problem characteristics

2. For high accuracy (tol ~ 1e-7):

   • DP5 becomes more competitive or faster
   • Higher order allows fewer steps

3. Memory usage:

   • BS3: Stores 4 values for dense output [y0, y1, f0, f1]
   • DP5: Stores 5 values for dense output [rcont1..rcont5]
   • Difference is minimal for most problems

Notes

• Benchmarks use std::hint::black_box() to prevent compiler optimizations
• Each benchmark runs multiple iterations to get statistically significant results
• Results may vary based on:
  • System load
  • CPU frequency scaling
  • Compiler optimizations
  • Problem characteristics (stiffness, nonlinearity, dimension)

Adding New Benchmarks

To add a new benchmark:

1. Create a new file in benches/ (e.g., my_benchmark.rs)
2. Add benchmark configuration to Cargo.toml:

   [[bench]]
   name = "my_benchmark"
   harness = false
   

3. Use the Criterion framework:

   use criterion::{criterion_group, criterion_main, Criterion};
   use std::hint::black_box;
   
   fn my_bench(c: &mut Criterion) {
       c.bench_function("my_test", |b| {
           b.iter(|| {
               black_box({
                   // Code to benchmark
               });
           });
       });
   }
   
   criterion_group!(benches, my_bench);
   criterion_main!(benches);