# 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

Glenn Young, Mathematics, gyoung19@kennesaw.edu

## Share

COinS

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.