Journal Article10.1016/J.ENGANABOUND.2017.10.021
A localized transform-based meshless method for solving time fractional wave-diffusion equation
Marjan Uddin,Kamran,Amjad Ali +2 more
27
TL;DR: In this paper, a hybrid transform-based localized meshless method is constructed for the solution of fractional diffusion-wave equations and the time stepping procedure is avoided to overcome the problem of time in-stability related to meshless methods.
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Abstract: In the present work, a hybrid transform-based localized meshless method is constructed for the solution of fractional diffusion-wave equations. The time stepping procedure is avoided to overcome the problem of time in-stability related to meshless methods. The issue of ill conditioning related to meshless differentiation matrices is resolved by incorporating small local system matrices. The time fractional diffusion-wave equation is selected to test the method. A clear improvement is observed in terms of stability, accuracy and ill-conditioning.
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Citations
A semi-analytical collocation Trefftz scheme for solving multi-term time fractional diffusion-wave equations
TL;DR: In this article, a semi-analytical boundary-only collocation technique for solving multi-term time-fractional diffusion-wave equations is presented, which is easy to implement and flexible for irregular domain problems.
48
A meshless local collocation method for time fractional diffusion wave equation
TL;DR: A radial basis function based local collocation method for solving time fractional diffusion-wave equation is presented and the present method is efficient and numerical results have nice agreements with theoretical result.
44
A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation
TL;DR: This is the first attempt to deal with 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation via a spectral approach and confirms that nonlocal numerical methods are best suited to discretize fractional differential equations as they naturally take the global behavior of the solution into account.
20
Effect of fractional temporal variation on the vibration of waves on elastic substrates with spatial non-homogeneity
TL;DR: In this paper , the effect of the fractional temporal variation on the vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral transform and the asymptotic approach was examined.
15
Numerical solution of multi-term time fractional wave diffusion equation using transform based local meshless method and quadrature
Jing Li,Linlin Dai,Kamran,Waqas Nazeer,Waqas Nazeer +4 more
- 01 Jan 2020
TL;DR: In this paper, a numerical method which combines Laplace transform with local radial basis functions method is presented, which eliminates the time variable with which the classical time stepping procedure is avoided, because in time stepping methods the accuracy is achieved at a very small step size, and these methods face sever stability restrictions.
14
References
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
9K
Multiquadrics--a scattered data approximation scheme with applications to computational fluid-dynamics-- ii solutions to parabolic, hyperbolic and elliptic partial differential equations
TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.
2.1K
Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
1.8K
An algorithm for selecting a good value for the parameter c in radial basis function interpolation
TL;DR: It is shown, numerically, that the value of the optimal c (the value of c that minimizes the interpolation error) depends on the number and distribution of data points, on the data vector, and on the precision of the computation.
981
The Accurate Numerical Inversion of Laplace Transforms
TL;DR: Inversion of almost arbitrary Laplace transforms is effected by trapezoidal integration along a special contour as mentioned in this paper, in which the number n of points to be used is one of several parameters, in most cases yielding absolute errors of order 10 for n = 10.