We then calculate the wave function of the time fractional Schrdinger using the inverse Laplace transform together considering the Schouten-Vanderpol theorem and some special circumstances of the problem. The o
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Techniques such as the Homotopy perturbation method,9 Iterative Laplace transform method,10,11 Collocation Technique,[12], [13], [14], [15] Fractional Reduced Differential Transformation Method16 and Differential Quadrature Method17 have shown promise in deriving solutions for nonlinear dynamics ...
Numerical Inversion of the Laplace Transform using the Talbot method. (Python recipe) 4 This is a fast and highly accurate numerical method for the inversion of the Laplace transform Python, 65 lines Download Copy to clipboard 1 2 3 4
the modal equation was solved within the frequency domain, using a Laplace transform, to arrive at a closed-form solution. Finally, the displacement, velocity and acceleration responses were obtained within the time domain by an inverse Laplace transform, and subsequent derivation with respect to tim...
This method involves an initial multi-scaling law to partition the numerical model (written in Python) and minimize computations at the meso-scale, while employing classical FEM at the macro-scale (part-scale) with the assistance of the Abaqus solver. The solver accounts for non-linear heat ...
The python implementation of the fixed-point solver relies on the API of the finite element package FEniCS (cf. [50, 51]). The implementation can be found in [52]. Energy-Variational Solutions to the Ericksen–Leslie Equations Page 37 of 44 11 Fig. 3 Experiment 4.1, model (33a)–(33b...
being 𝐹(𝑠)=𝑠−𝛼 the Laplace transform of the kernel 𝑡𝛼−1/Γ(𝛼) in (1). The assumptions that make possible this generalization of LMMs are that the generating function 𝛿(𝜉) has no zeros in the closed unit disc |𝜉|≤1, except for 𝜉=1, and |arg𝛿(...