Date of Award
Spring 2012
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
James Lambers
Committee Chair Department
Mathematics
Committee Member 2
Joseph Kalibal
Committee Member 2 Department
Mathematics
Committee Member 3
Haiyan Tian
Committee Member 3 Department
Mathematics
Abstract
Technological advancements have allowed computing power to generate high resolution model s. As a result, greater stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components of the solutions to these systems are coupled and changing at widely varying rates, which present problems for time-stepping methods. Krylov Subspace Spectral methods, developed by Dr. James Lambers, bridge the gap between explicit and implicit methods for stiff problems by computing each Fouier coefficient from an individualized approximation of the solution operator. KSS methods demonstrate a high order of accuracy, but their efficiency needs to be improved. We will carry out an asymptotic study to determine how these approximations behave at high frequencies to develop a formula to reduce the computation of each node while still achieving a high level of accuracy. Our numerical results will reveal that our method does prove to increase the efficiency as well as the accuracy of KSS methods.
Copyright
2012, Elisabeth Marie Palchak
Recommended Citation
Palchak, Elisabeth Marie, "Rapid Approximation of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis of Gaussian Node Placement" (2012). Master's Theses. 510.
https://aquila.usm.edu/masters_theses/510