Title

FINITE VOLUME METHODS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH DELTA-SINGULARITIES

Author

Nattaporn Chuenjarern, Michigan Technological University

Date of Award

2015

Document Type

Master's report

Degree Name

Master of Science in Mathematical Sciences (MS)

College, School or Department Name

Department of Mathematical Sciences

Advisor

Yang Yang

Abstract

In this work, we study hyperbolic conservation law in one space dimension with δ-singularities as the initial data. We use finite volume methods to find the sizes of pollution region. Firstly, we study finite volume method (FVM) with linear weights and weighted essentially non-oscillatory (WENO) scheme and apply both methods to linear partial differential equations without singularities to check the accuracy. Then we use both methods to find the numerical solutions and compute errors of linear equations with δ-singularities. Lastly, we use such results to find the size of pollution region of each method. These results show that the size of the pollution region is approximately of the order O(Δx^1/2), where Δx is the spatial mesh size.

Recommended Citation

Chuenjarern, Nattaporn, "FINITE VOLUME METHODS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH DELTA-SINGULARITIES", Master's report, Michigan Technological University, 2015.

https://doi.org/10.37099/mtu.dc.etds/971