An update strategy for numerically solving boundary value problems
LE3 .A278 2009
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
Certain types of boundary value problems have solutions which exhibit special properties making it difficult to approximate numerically. The solutions on these regions have rapidly changing features. We explore a method of arriving at an approximation to the solution by choosing a mesh of points across the domain and estimating the value of the solution at those points. One then chooses where it would be beneficial to place additional mesh points along the domain to achieve a better approximation. In this thesis we develop a method to identify the regions requiring a more refined mesh. We then use the Sherman-Morrison-Woodbury formula and the Block Matrix Inverse formula to continually update our approximation to the solution until a user-defined error tolerance has been achieved across the whole domain.
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