Dr. Michelle Ghrist's research in numerical analysis bridges mathematics and computer science. She and her students develop and analyze algorithms to approximate solutions for differential equations. These equations are used in medical imaging, satellite and planetary orbital mechanics, and weather modeling. The goal is to create methods that are more accurate and stable than current ones, without increasing computational costs.
Analysis involves visualizing how different numerical methods behave. Using a complex plane -- a type of mathematics graph where each point represents a complex number -- the researchers plot the region where a particular method for solving differential equations works well and gives stable results: a stability domain. Plotting these stability domains shows which methods are stable for multiple problems. By looking for the patterns and understanding the strengths and limitations of different methods, the research can guide scientists towards the best algorithms that fits their needs.
Dr. Ghrist's numerical analysis research group typically has 2 or 3 student researchers at any time since 2018. She also supervises undergraduates on mathematical modeling. Her students have presented their work at the national Joint Mathematics Meetings, and regional conferences like Southern California Conferences for Undergraduate Research (SCCUR), Mathematical Association of America (MAA), Society for Industrial and Applied Mathematics (SIAM), Pacific Inland Mathematics Undergraduate Conference (PiMUC) and the Spokane Intercollegiate Research Conference. Three students have won outstanding poster awards, and the team is preparing a series of publications based on their research.
