Stable quartic spline integration method for solving stiff ordinary differential equations

摘要

The convergence and stability analysis of a quartic C2-spline collocation method for solving initial value problems, including stiff differential equations, will be considered. Letting the interior collocation point xi−1+β=xi−1+βh be dependent on some parameter β∈(0,1) it will be shown that the method possesses convergence rate of order 4 if β∈[1/2,1) and is strongly unstable if β<1/2. Moreover, a wider region of absolute stability is achieved if β→1−0.