Implementation of DIMSIMs for stiff differential systems (Q1612461)

The author describes a variable-step variable-order experimental code for the numerical solution of stiff differential systems. The code is based on A-stable diagonally implicit multistage integration methods of order 1, 2 and 3. Special issue are discussed: reliable estimation of the local discretization error, construction of continuous interpolants, choice of initial stepsize and order. The numerical experiments indicate that the new code outperforms the Matlab code for stiff ordinary differential equations (ODEs) on systems whose Jacobian has eigenvalues which are close to the imaginary axis.