AMF-Runge-Kutta formulas and error estimates for the time integration of advection diffusion reaction PDEs

作者：Gonzalez Pinto S^*; Hernandez Abreu D; Perez Rodriguez S

来源：Journal of Computational and Applied Mathematics, 2015, 289: 3-21.

DOI：10.1016/j.cam.2015.03.048

• Evolutionary advection-diffusion-reaction
• partial differential equations
• Approximate Matrix Factorization
• Runge-Kutta Radau IIA methods
• Finite differences
• Stability and convergence

The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) for the time integration of evolutionary Partial Differential Equations (PDEs) of Advection Diffusion Reaction type semi-discretized in space is considered. The methods are based on very few inexact Newton Iterations applied to Implicit Runge-Kutta formulas by combining the use of a natural splitting for the underlyinglacobians and the Approximate Matrix Factorization (AMF) technique. This approach allows a very cheap implementation of the Runge-Kutta formula under consideration. Particular AMF-RK methods based on Radau IIA formulas are considered. These methods have given very competitive results when compared with important formulas in the literature for multidimensional systems of non-linear parabolic PDE problems. Uniform bounds for the global time-space errors on semi-linear PDEs when simultaneously the time step-size and the spatial grid resolution tend to zero are derived. Numerical illustrations supporting the theory are presented.

• 出版日期2015-12-1