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Title: Numerical Solutions of Time-Fractional Partial Differential Equations Using Spline Collocation Techniques.
Authors: Amin, Muhammad
Keywords: Physical Sciences
Issue Date: 2020
Publisher: National College of Business Administration & Economics, Lahore.
Abstract: This work is concerned with the numerical study of some time fractional partial differential equations by means of different spline collocation techniques. The Caputo's definition has been considered for time fractional derivative of order α belonging to (0,1] and (1,2]. Approximate solution of two very important mathematical models involving fourth order time fractional partial differential equations have been investigated. The presented algorithms utilize non polynomial quintic spline functions, composed of polynomial and trigonometric parts, usual finite difference approximations for spatial and temporal discretizations respectively. The trigonometric part of non-polynomial quintic spline possesses C∞ differentiability which takes care of the loss of smoothness caused by polynomial part. Furthermore, numerical methods based on redefined extended B-spline functions and usual finite difference formulation have also been developed for numerical solution of time fractional Klein-Gordon equation and multi term time fractional telegraph equation. For spatial discretization, redefined extended B-spline functions have been used, whereas, to interpolate the solution curve along time grid, usual finite difference approximations are brought into play. Theoretically as well as numerically, the proposed numerical techniques are proved to be convergent and unconditionally stable. To validate this work, some test problems have been considered and the numerical results are compared with existing computational techniques. It is concluded that due to the straightforward and simple application, our proposed techniques return more accurate outcomes as compared to other numerical schemes on the topic.
Gov't Doc #: 20255
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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