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
","abstract_html":"<p>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</p>","abstract_has_math":false,"creators":["Charbe, Nirmohi"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dr. James Lambers","Dr. Bernd Schroeder","Dr. Huiqing Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-06-01T07:00:00Z","date_published":"2023-06-01T07:00:00Z","updated_at":"2026-07-24T05:45:47Z","subjects":["kss","computational neuroscience","numerical methods","second order PDE","cable equation","Analysis","Applied Mathematics","Numerical Analysis and Computation","Other Applied Mathematics","Other Biochemistry, Biophysics, and Structural Biology","Partial Differential Equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/981","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. James Lambers","Dr. Bernd Schroeder","Dr. Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Charbe, Nirmohi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2023-06-27T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["kss","computational neuroscience","numerical methods","second order PDE","cable equation","Analysis","Applied Mathematics","Numerical Analysis and Computation","Other Applied Mathematics","Other Biochemistry, Biophysics, and Structural Biology","Partial Differential Equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/981"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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
"]},{"key":"dc:title","label":"Title","values":["SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS"]}]}],"canonical_facts":{"dc:contributor":["Dr. James Lambers","Dr. Bernd Schroeder","Dr. Huiqing Zhu"],"dc:creator":["Charbe, Nirmohi"],"dc:date.available":["2023-06-27T07:00:00Z"],"dc:description.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
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/981"],"dc:subject":["kss","computational neuroscience","numerical methods","second order PDE","cable equation","Analysis","Applied Mathematics","Numerical Analysis and Computation","Other Applied Mathematics","Other Biochemistry, Biophysics, and Structural Biology","Partial Differential Equations"],"dc:title":["SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:47Z"}