On Adaptive Patankar Runge–Kutta methods

We apply Patankar Runge–Kutta methods to y′ = M(y)y and focus on the case where M(y) is a graph Laplacian as resulting scheme will preserve positivity total mass. The second order Heun method tested using four test problems (stiff non-stiff) cast into this form. local error estimated step size chosen adaptively. Concerning accuracy efficiency, results are comparable those obtained with traditional L-stable, Rosenbrock method.