Date of Award
Fall 10-2021
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
C. S. Chen
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Haiyan Tian
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.
The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.
The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.
Recommended Citation
Shimp, Chandler, "Multi-valued Solutions for the Equation of Motion, Darcy-Jordan Model, as a Cauchy Problem: A Shocking Event" (2021). Master's Theses. 866.
https://aquila.usm.edu/masters_theses/866
Included in
Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Partial Differential Equations Commons, Theory and Algorithms Commons