Comparing Explicit and Implicit Numerical Schemes for a 1D Moving Boundary Problem
Disciplines
Dynamic Systems | Numerical Analysis and Computation | Partial Differential Equations
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.
Academic department under which the project should be listed
CSM - Mathematics
Primary Investigator (PI) Name
Yizeng Li
Additional Faculty
Glenn Young, Mathematics, gyoung19@kennesaw.edu
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.