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Application of the discrete regularization method to the inverse of the chord vibration equation. (English) Zbl 1387.74056

Summary: The inverse problem of the initial condition about the boundary value of the chord vibration equation is ill-posed. First, we transform it into a Fredholm integral equation. Second, we discretize it by the trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the data. In addition, the tiny error of right data causes the huge concussion of the solution. We cannot obtain good results by the traditional method. In this paper, we solve this problem by the Tikhonov regularization method, and the numerical simulations demonstrate that this method is feasible and effective.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
65F22 Ill-posedness and regularization problems in numerical linear algebra
74S30 Other numerical methods in solid mechanics (MSC2010)
45B05 Fredholm integral equations
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