An error embedded method based on generalized Chebyshev polynomials

In this paper, we develop an error embedded method based on generalized Chebyshev polynomials for solving stiff initial value problems. The solution and the error at each integration step are calculated by generalized Chebyshev polynomials of two consecutive degrees having overlapping zeros, which enables us to minimize overall computational costs. Further the errors at each integration step are embedded in the algorithm itself. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 6th order convergence and an almost L-stability. We assess the proposed method with several numerical results, showing that it uses larger time step sizes and is numerically more efficient.