ode_moshier, a C code which solves systems of ordinary differential equations (ODE). Two main methods are implemented, the Adams-Bashforth-Moulton integrator, and the Runge-Kutta integrator, by Steven Moshier.
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ode_moshier is available in a C version.
c_ode_solver, a C code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.
Steven Moshier