Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/16506
Title: Trigonometric Cubic B-Spline Collocation Method Based on Finite Difference Schemes for Numberical Solutions of Time Fractional Partial Differential Equations
Authors: Yaseen, Muhammad
Keywords: Physical Sciences
Mathematics
Issue Date: 2019
Publisher: University of Sargodha, Sargodha.
Abstract: The central point of this thesis is to present numerical procedures dependent on a relatively new B-spline called the cubic Trigonometric B-spline (CTBS) and the finite difference methods (FDM) for the time-fractional sub-diffusion, time-fractional diffu sion, time-fractional diffusion-wave, time-fractional telegraph, time-fractional Burg ers’ and the time-fractional Klein-Gordon equations. An extraordinary consideration has been given to the stability and convergence analysis for each model to affirm that the errors do not amplify. The standard finite difference formulation is utilized to approximate the time-fractional derivatives (in Riemann-Liouvile or Caputo sense) while the derivatives in space are discretized using the CTBS. One essential contribution of this thesis is to present a new linearization technique for the nonlinear advection term showing up in the time-fractional Burgers’ equation. This linearization technique is very productive and has significantly decreased the computational cost. Numerical experiments are performed in support of our theoretical analysis and the obtained numerical findings are compared with those present in the literature. It is also emphasized that the presented numerical schemes are applicable to a variety of linear and nonlinear fractional partial differential equations.
Gov't Doc #: 21386
URI: http://prr.hec.gov.pk/jspui/handle/123456789/16506
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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