Project Title

Comparing Explicit and Implicit Numerical Schemes for a 1D Moving Boundary Problem

Academic department under which the project should be listed

CSM - Mathematics

Faculty Sponsor Name

Yizeng Li

Additional Faculty

Glenn Young, Mathematics, gyoung19@kennesaw.edu

Abstract (300 words maximum)

When modeling natural systems, boundary value problems naturally arise. Modeling large systems typically requires the aid of a computer to approximate an otherwise unobtainable solution. When choosing a numerical scheme, stability and accuracy are of great concern. Typically, explicit methods are easier to implement but have stricter stability conditions. On the other hand, Implicit methods can maintain stability and save on computational time using large timesteps. Whether to choose explicit or implicit methods depends on the problem, and sometimes a combination of both works best. Our goal is to find a balance of stability, accuracy, and computation time. Two schemes are developed in MATLAB and are used to solve the same 1D moving boundary problem. In this talk we discuss the error, stability, and time efficiency of two numerical schemes for a 1D moving boundary problem modeling cell migration.

Disciplines

Dynamic Systems | Numerical Analysis and Computation | Partial Differential Equations

Project Type

Oral Presentation (15-min time slots)

How will this be presented?

Yes, in person

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Comparing Explicit and Implicit Numerical Schemes for a 1D Moving Boundary Problem

When modeling natural systems, boundary value problems naturally arise. Modeling large systems typically requires the aid of a computer to approximate an otherwise unobtainable solution. When choosing a numerical scheme, stability and accuracy are of great concern. Typically, explicit methods are easier to implement but have stricter stability conditions. On the other hand, Implicit methods can maintain stability and save on computational time using large timesteps. Whether to choose explicit or implicit methods depends on the problem, and sometimes a combination of both works best. Our goal is to find a balance of stability, accuracy, and computation time. Two schemes are developed in MATLAB and are used to solve the same 1D moving boundary problem. In this talk we discuss the error, stability, and time efficiency of two numerical schemes for a 1D moving boundary problem modeling cell migration.

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