Solvability of concatenated Runge-Kutta equations for second-order nonlinear PDEs

Authors:
Jialin Hong;Chol Sim;Xiuling Yin
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, P.O. Box 2719, Beijing 100190, PR China;Institute of Mathematics, Academy of Sciences, Pyongyang, Democratic People's Republic of Korea;Department of Mathematics, Dezhou University, Dezhou 253023, Shandong, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

In this paper, we consider the solvability of concatenated Runge-Kutta (CRK) equations, which are the nonlinear algebraic equations arising from CRK methods applied to some kind of second-order nonlinear partial differential equations. To guarantee the existence and uniqueness of the solution of CRK equations, temporal and spatial step-sizes of CRK methods should be chosen appropriately. Under different assumptions, with the homotopy continuation method, we choose different step-sizes to ensure the solvability of CRK equations.