Extractum Opii Liquidum is a liquid extract of opium. Its physical form and specified strength differ from those of the solid extract.^[ref]

Vinum Opii is an opium-containing medicinal wine. The wine vehicle and the extracted material define the historical liquid together.^[ref]

Tinctura Camphorae cum Opio is a tincture combining camphor and opium. Its multiple ingredients distinguish it from a plain opium tincture.^[ref]

Pilula Opii is an opium pill preparation. A finished pill contains a specified preparation rather than being a direct synonym for the crude plant exudate.^[ref]

Pilula Plumbi cum Opio is a historical lead-containing pill combined with opium. The inclusion of a lead compound is a defining compositional feature, not a modern endorsement.^[ref]

Pulvis Cretae Aromaticus cum Opio is an aromatic chalk-and-opium compound powder. Mineral, aromatic and opium-containing components have different roles in its composition.^[ref]

Pulvis Ipecacuanhae cum Opio is a compound powder combining ipecacuanha and opium. Its ingredients make it distinct from either source material alone.^[ref]

Pulvis Kino cum Opio is a compound powder combining kino and opium. The preparation joins chemically different plant-derived materials rather than one isolated drug.^[ref]

Trochisci Opii is opium-containing lozenges. A unit lozenge and a mass of crude opium represent different pharmaceutical quantities.^[ref]

Enema Opii is an opium-containing rectal liquid preparation. The route and formulation distinguish it from an oral preparation.^[ref]

Emplastrum Opii is an opium-containing plaster. The adhesive or supporting mass is part of the finished preparation rather than an inert synonym for its active ingredients.^[ref]

Linimentum Opii is an opium-containing liniment. An external liquid formulation differs from an oral tincture even when the same source drug is named.^[ref]

Unguentum Gallae cum Opio is an ointment combining gall material and opium. Its compound identity joins an astringent material with an opioid-containing material.^[ref]

Confectio Opii is an opium-containing confection. The mixed vehicle distinguishes it from crude opium and from a purified opioid.^[ref]

Morphine is an opioid agonist used as an important reference substance in the study of analgesia. Its effects include changes in pain processing and breathing. A desired effect and other physiological actions can arise from the same drug exposure.

Codeine is an opioid whose effects depend partly on metabolic conversion to morphine. Variation in drug metabolism can therefore change the relation between an administered amount and the resulting active exposure.

Adaptation following repeated exposure, affecting response to an opioid. It does not eliminate overdose risk.

A one-step method approximates an ordinary differential equation using the current approximate solution and evaluations within the next step. The function $\Phi$ is its increment function. A Runge-Kutta method may use several intermediate stages while remaining a one-step method: it does not require additional previous solution values as a linear multistep method does. Its consistency error is the exact-start update defect divided by $h$.

Numerical differentiation estimates derivatives from finitely many function values, often by differentiating an interpolation polynomial or using a finite difference. Its error combines truncation error from the formula with errors already present in the sampled values and additional roundoff error. Decreasing the sample spacing can decrease truncation error while increasing the effect of uncertain values. This tradeoff is explained by the ill-posedness of numerical differentiation when only an absolute value-error bound is available.

A time-stepping method approximates the evolution of an ordinary differential equation by successive updates at discrete times. It can be applied after a spatial finite element method has converted a time-dependent partial differential equation into an ordinary differential equation system. The implicit time-stepping method is one class of such methods.