کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6422391 | 1632002 | 2015 | 19 صفحه PDF | دانلود رایگان |
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 underlying Jacobians 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.
Journal: Journal of Computational and Applied Mathematics - Volume 289, 1 December 2015, Pages 3-21