Dormand

Dormand is a surname that has become associated with a prominent family of numerical methods for solving ordinary differential equations, known as the Dormand–Prince methods. The methods were developed by John R. Dormand and Philip J. Prince in the 1980s to provide efficient adaptive-step integrators based on explicit Runge-Kutta formulas. The name in this context is used to credit the authors of the method.

The Dormand–Prince family consists of embedded Runge-Kutta pairs, designed to produce two estimates of different orders from a single step, enabling automatic control of the local truncation error. The best known member is the Dormand–Prince 5(4) method, which computes a fifth-order accurate solution with a fourth-order error estimate. Because the error estimate is inexpensive to obtain, the step size can be adjusted to maintain a user-specified accuracy while minimizing computational work.

These methods are widely used in scientific computing. They underpin popular ODE solvers in software such as MATLAB's ODE45 and the Python SciPy library's solve_ivp with the RK45 option, which implement the Dormand–Prince 5(4) scheme. They are not ideal for stiff systems, where implicit methods are generally preferred, but for non-stiff problems they offer a reliable balance of accuracy and performance.

In addition to the algorithm, Dormand appears as a surname in mathematical literature and biographies of researchers who contributed to numerical analysis.