A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation

Details A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation

2011-12-21

arxiv.org/abs/1112.4921v1

Numerical Methods for Partial Differential Equations 21(5)pp.998-1015, 1 Sep 2005

Mathematics

Numerical Analysis

Scientific paper

10.1002/num.20094

In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of the initial-value problem with smooth initial conditions in an open sphere around the origin, where the internal and external damping coefficients are constant, and the nonlinear term follows a power law. We prove that our scheme is consistent of second order when the nonlinearity is identically equal to zero, and provide a necessary condition for it to be stable order n. Part of our study will be devoted to compare the physical effects of the damping coefficients.

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