Content Details | NUML Online Research Repository

Content Details

Back to Department Listing

Title Modification of Finite Difference Scheme for Time-fractional Hyperbolic Problem with Stability Analysis

Author(s) Muhammad Mehtab

Abstract In this thesis the modification of finite difference scheme for the time-fractional wave problem with stability analysis for one- and two-dimensional time fractional wave equations (1D-TFWE and 2D-TFWE, respectively) on a finite domain is investigated. In the empire of mathematical physics and engineering, it has been recently discovered that the majority of physical processes give fractional order wave equations when modelled. To examine the techniques for solving fractional order wave equations and turn this scenario into an attractive research project, the precise solutions are crucial. Furthermore, problems in physics, environmental science, biology, and other fields of application have been modeled using fractional wave equations. For the (1D-TFWE) and (2D-TFWE), a Crank-Nicolson difference approximation is proposed. We explored the method's stability and convergence using mathematical induction. Finally, some numerical examples are shown. The numerical result and our theoretical analysis accord quite well.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2024-01-06

Subject Mathematics

Publisher

Contributor(s)

Format

Identifier

Source

Relation

Coverage

Rights