Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Probabilistic Linear Multistep Methods
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use s-step Adams-Bashforth multistep (s=3 or s=5) instead of s=1 in probabilistic integrator on Chua circuit | probabilistic Adams-Bashforth integrator · Chua circuit (t up to 1000, h=0.01) | time until numerical path diverges from truth | Helped |
| Increase AB order from 1 to 3 to 5 at fixed step size, with no additional f evaluations beyond one-step method | probabilistic Adams-Bashforth integrator · Lotka-Volterra model, x-component error | convergence order of mean absolute error vs step size | Helped |
| Higher-order multistep (s=2,3) vs one-step: error distribution around zero | probabilistic Adams-Bashforth integrator · Lotka-Volterra model, 200 realisations | sign/bias of error | Mixed |
| Set noise scale alpha to y^(s+1) estimate via backward differences of f instead of unknown derivative, so the posterior std matches local truncation error | probabilistic Adams-Bashforth integrator · theoretical (no numerical comparison reported) | posterior std vs local truncation error | No clear effect |
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