Resources Numerical accuracy
Calculations
Every calculation under our calculation policies: what it works out, its formula and the precision it runs at. Open one to see its code as it is in the released app.
Calculations
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Resistive element laws
The flow through a resistor, damper, orifice, diode or user law for a given difference across it.
resistor: i = v ÷ R; orifice: i = v ÷ √(K √(v² + ε²)); diode: i = Is (e^(v ÷ nVt) − 1), a straight line above 40 nVt
Lumped system models model.js Every app64-bit -
Storage elements
Capacitors, masses, tanks, inductors and springs: what they store and how it enters the equations.
capacitive: i + d(C v)/dt = 0; inductive: v + d(L i)/dt = 0; spring: L = 1 ÷ k
Lumped system models model.js Every app64-bit -
Reported flow through an element
The current, heat flow, flow or force reported for an element.
the element's law at the solved state; diode: Is (e^(min(v, 40 nVt) ÷ nVt) − 1)
Lumped system models model.js Every app64-bit -
Dense linear solve
Solves the Newton step.
Gaussian elimination with partial pivoting
Lumped system models solve.js Every app64-bit -
Newton iteration
Finds the state that satisfies the equations at one time.
J_ij = (F_i(x + h e_j) − F_i(x − h e_j)) ÷ 2h, h = 1e-7 × max(|x_j|, 1); stop when |Δxᵢ| ≤ rtol |xᵢ| + atol + 1e-11 × max(1, largest |x|)
Lumped system models solve.js Every app64-bit -
Operating point
The steady state, or the state set by the given initial values.
one Newton solve from zero
Lumped system models solve.js Every app64-bit -
One time step
The state one step later.
trapezoid: (2 ÷ h)(S − S₀) − Ṡ₀ + g = 0; backward Euler: (1 ÷ h)(S − S₀) + g = 0
Lumped system models solve.js Every app64-bit -
Step-size control
Chooses the time step from an estimate of the error, when adaptive stepping is on.
err = max |x(two half steps) − x(one step)| ÷ (rtol |x| + atol), ÷ 3 for the trapezoid; h ← h × clamp(0.9 err^(−1/3), 0.2, 5)
Lumped system models solve.js Every app64-bit -
Value between stored times
A node value at a time between two computed points.
y = y₀ + (y₁ − y₀)(t − t₀) ÷ (t₁ − t₀)
Lumped system models solve.js Every app64-bit -
Parameter expressions
The value of a parameter written as an expression, such as 2*3.3e3.
numbers, parameters, + − × ÷ ^, brackets, pi
Lumped system models modelica.js Every app64-bit -
Thermal conductance to resistance
A thermal conductor from a model file as the engine's thermal resistance.
R = 1 ÷ G
Lumped system models modelica.js Every app64-bit
A calculation is added only after its source was read. Each statement can be checked in the code shown on its policy's page; the app repositories are public. When a release changes a calculation, its page says so until it has been read again.