Compressed solving: A numerical approximation technique for elliptic PDEs based on Compressed Sensing

A one-dimensional steady state bio-heat transfer model of temperature distribution in cylindrical living tissue is discussed using numerical approximation technique the Galerkin Finite element method.We observe the effects of the thermal conductivity of the thermal system. The results show that the derived solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment. Journal of Advanced College of Engineering and Management, Vol. 1, 2015, pp. 45-50

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A freely damped oscillating fractional dynamic system modeled by fractional Euler–Lagrange equations

Journal of Vibration and Control ◽

10.1177/1077546316685228 ◽

2017 ◽

Vol 24 (7) ◽

pp. 1228-1238 ◽

Cited By ~ 7

Author(s):

Adel Agila ◽

Dumitru Baleanu ◽

Rajeh Eid ◽

Bulent Irfanoglu

Keyword(s):

Fractional Derivative ◽

Dynamic Systems ◽

Numerical Approximation ◽

Inertia Force ◽

Approximation Technique ◽

Lagrange Equations ◽

Damping Force ◽

Fractional Damping ◽

Integer Representation ◽

Fractional Orders

The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler–Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.

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Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.11-m11168 ◽

2013 ◽

Vol 5 (1) ◽

pp. 78-89 ◽

Cited By ~ 14

Author(s):

Ahmad Shirzadi ◽

Leevan Ling

Keyword(s):

Error Analysis ◽

Basis Function ◽

Numerical Approximation ◽

Weak Form ◽

Elliptic Pdes ◽

Double Precision ◽

Step Functions ◽

Mlpg Method ◽

Local Weak Form ◽

Good Agreement

AbstractThis paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

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