Fixed-Step ODE4 and ODE5 Algorithms: Implementation and Performance

The article discusses fixed-step ODE4 and ODE5 algorithms that follow similar usage patterns as MATLAB's ode45 solver. The primary distinction lies in their function signatures: ode45 employs [t, y] = ode45() while ODE4/ODE5 algorithms use y = ode4(). These fixed-step methods implement numerical integration techniques (typically 4th and 5th order Runge-Kutta variants) with predetermined step sizes throughout the computation. It's important to note that due to their fixed-step nature, these algorithms may produce different results compared to variable-step methods like ode45, as they maintain constant intervals between solution points without adaptive error control. A significant advantage is that ODE4 and ODE5 algorithms demonstrate faster computational speeds than ode45, since the fixed-step approach eliminates the overhead of step size adjustment and error estimation procedures, resulting in a more straightforward and efficient calculation process. When computational efficiency is prioritized for ODE problems, especially in real-time applications or scenarios where consistent time steps are required, ODE4 and ODE5 algorithms present viable alternatives to variable-step solvers.