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Title: Meshless Simulation of Linear and Non-linear Fractional Partial Differential Equations
Authors: , Mehnaz
Keywords: Physical Sciences
Issue Date: 2022
Publisher: University of Engineering & Technology Peshawar
Abstract: In this thesis, the local and global radial basis functions based collocation schemes are implemented to find the numerical solution of the linear and non-linear fractional par tial differential equations, including time fractional partial differential equations and space fractional partial differential equations. In case of the time fractional partial differen tial equations, the time derivative is approximated by the Caputo fractional derivative and the space derivatives are approximated by θ−weighted scheme. While in the space fractional partial differential equations, the Caputo as well as the Riemann-Liouville frac tional derivatives of radial basis functions are evaluated to approximate the space fractional derivatives. Moreover, the numerical solution and the characteristic study of the shock waves colli sion is discussed, which is discussed for the first time. By applying the extended Poincare Lighthill-Kuo technique, two-sided Korteweg-deVries-Burgers equations and their corre sponding phase shifts for the shock waves are derived. In comparison of the shocks so lutions with observation data, it was found out that the amplitude of shocks would un derestimate in a range of 20%. To reduce this variation, in the next step, the derived two-sided Korteweg-deVries-Burgers equations are converted to two-sided time-fractional Korteweg-deVries-Burgers equations by semi inverse method, which are then solved nu merically by local meshless method. The effects of the ratio of electron temperature to positron temperature, the spectral indices (κe, κp) and fractional concentration of positron component on the phase shift are also examined. Due to the easy implementation of the radial basis functions to the higher dimensions and complex geometries, the solution at the irregular domains and non-uniform nodes is also considered in addition to the regular domain and uniform nodes. The influence of the fractional derivative order over the solution is discussed with the help of the figures. It is shown that the amplitude and steepness of the solution graph changes by changing the fractional order.
Gov't Doc #: 25275
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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