Finally, let us note that presented polynomial version of the numerical-analytic method in this article can be extended to more general nonlinear boundary value problems studied in [14].
For a boundary value problem, the numerical-analytic approach usually replaces the problem by a family of initial value problems for a suitably perturbed system containing a vector parameter which most often has the meaning of the initial value of the solution.
In its original form (see, e.g., [2], [3] for references), the numerical-analytic approach that we are dealing with suggests one to look for a solution of (1), (2) among the limit functions of certain n -parametric family of sequences possessing property (2) (see, e.g., [2], [3]).
Afterwards, this method has been successfully applied to deal with various inverse problems, e.g. the problem of a numerical pseudodifferential operator [21], the problem of numerical analytic continuation [22], the Cauchy problem for the Helmholtz equation [23], etc.
E. Rabani, D. R. Reichman, G. Krilov and B. J. Berne, The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen.
Numerical analytic results imply that the cable loosening appears in the bottom cables of the multi-cable system and the dynamic response of the bridge is slightly increased.
It is worth mentioning that Feng and Ning [32] used a Meyer wavelet regularization method for solving numerical analytic continuation and presented the Hölder-type stability estimates.
The validity of numerical simulation for discontinuity effects is confirmed by comparison of the numerical and analytic results.
assessing the accuracy of the method by measuring the difference between the numerical and analytic solutions u h and u, respectively.
In this article, we introduce the Chebyshev polynomial version of the known numerical-analytic method based on successive iterations.
Compared with the numerical methods, the analytic method presented in this paper is simple in computing the longitudinal and radial resonance frequencies and in analyzing the coupled vibrational modes of the piezoelectric ceramic disks with central holes.
