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Computation of the Laplace inverse transform by application of the wavelet theory. (English) Zbl 1035.65159

Summary: An efficient and robust method of solving Laplace inverse transform is proposed based on the wavelet theory. The inverse function is expressed as a wavelet expansion with rapid convergence. Several examples are provided to demonstrate the methodology. As an example of application, the proposed inversion method is applied to the dynamic analysis of a single-degree-of-freedom spring-mass-damper system whose damping is described by a stress-strain relation containing fractional derivatives. The results are compared with previous studies.

MSC:

65R10 Numerical methods for integral transforms
44A10 Laplace transform
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T40 Numerical methods for trigonometric approximation and interpolation
74B20 Nonlinear elasticity
65T60 Numerical methods for wavelets
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