Date of Award
Summer 6-2023
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Bernd Schroeder
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and other than Cable Equation to the study of Neurodegenerative diseases like multiple sclerosis, Alzheimer’s, Parkinsons etc. The ultimate goal would be to be able to study a broad application of numerical methods to understand features of the human brain and its functions without involving medically invasive procedures. ii
Recommended Citation
Charbe, Nirmohi, "SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS" (2023). Master's Theses. 981.
https://aquila.usm.edu/masters_theses/981
Included in
Analysis Commons, Computational Neuroscience Commons, Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Other Biochemistry, Biophysics, and Structural Biology Commons, Partial Differential Equations Commons