Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations
A new class of stable methods for solving ordinary differential equations (ODEs) is introduced. This is based on combining the Local Linearization (LL) integrator with other extant discretization methods. For this, an auxiliary ODE is solved to determine a correction term that is added to the LL approximation. In particular, combining the LL method with (explicit) Runge Kutta integrators yields what we call LLRK methods. This permits to improve the order of convergence of the LL method without loss of its stability properties. The performance of the proposed integrators is illustrated through computer simulations.
KeywordsPhase Portrait Local Linearization Matrix Exponential General Linear Method Local Linearization Approximation
- 3.Biscay, R.J., De la Cruz, H., Carbonell, F., Ozaki, T., Jimenez, J.C.: A Higher Order Local Linearization Method for Solving Ordinary Differential Equations. Technical Report, Instituto de Cibernetica, Matematica y Fisica, La Habana (2005)Google Scholar
- 8.Higham, N.J.: The scaling and squaring method for the matrix exponential revisited. Numerical Analysis Report 452, Manchester Centre for Computational Mathematics (2004)Google Scholar