The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids

Backward differential formulae (BDF) are the basis of the highly efficient schemes for the numerical solution of stiff ordinary differential equations for decades. An alternative multistep scheme (RBDF) based on barycentric rational interpolation is proposed. Specifically, robust new methods of orders 1 to 5 are derived. The local truncation error is analyzed for variable stepsizes in order to implement a variable order, variable stepsize prototype in Matlab. Aspects of the implementation are addressed in detail. Numerical experiments illustrate that the RBDF code compares well with Matlab’s ode15s.