. Author manuscript; available in PMC: 2016 Mar 1.

Published in final edited form as: Cell Mol Bioeng. 2015 Mar;8(1):119–136. doi: 10.1007/s12195-014-0363-6

Table 2.

Relative Computational Speeds for Case Study 1

	100 × 100 Simulation Grid ~5,000 Agents			200 × 200 Simulation Grid ~10,000 Agents
	ODE Numerical Method			ODE Numerical Method

PDE Numerical Method	FE (Δt = 0.6s)	RK4 (Δt = 6s)	TR (Δt = 6s)	FE (Δt = 0.6s)	RK4 (Δt = 6s)	TR (Δt = 6s)
FTCS (Δt = 6s)	1.0	2.3	4.6	1.0	2.6	5.4
ADE (Δt = 30s)	1.8	4.3	12.8	1.2	3.9	7.7
SM (Δt = 120s)	1.8	5.5	22.7	1.2	5.2	23.6

FTCS – Forward Time Central Space, ADE – Alternating Direction Explicit, SM – Spectral Method, FE – Forward Euler, RK4 – Runge-Kutta 4^th Order, TR – Tuneable Resolution

N=3 for all simulations. 100×100 – Relative Speed of 1.0 corresponds to 7589 s of simulation time, 200×200 – Relative Speed of 1.0 corresponds to 46907 s of simulation time