# Chapter 7, Tools for the Verification of Approximate Solutions

### Wayne H. Enright

• Figure 7.1 a Approximate solution produced by ode45 for predator-prey problem, Solution Plot
• Figure 7.1 b Approximate solution produced by ode45 for predator-prey problem, Phase Portrait
• Figure 7.2 a Approximate solution produced by ode45 for Lorenz problem, Solution Plot
• Figure 7.2 b Approximate solution produced by ode45 for Lorenz problem, Phase Portrait
• Figure 7.3 a ETOL(x) for ode45, predator-prey problem, TOL = 10-3
• Figure 7.3 b ETOL(x) for ode45, Lorenz problem, TOL = 10-6
• Figure 7.4 a ETOL(x) for ode45, predator-prey problem, TOL = 10-5
• Figure 7.4 b ETOL(x) for ode45, Lorenz problem, TOL = 10-8
• Figure 7.5 a ETOL(x) for ode45, predator-prey problem, TOL = 10-7
• Figure 7.5 b ETOL(x) for ode45, Lorenz problem, TOL = 10-10
• Figure 7.6 a Check 1, Check 2 and Check 4 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-3
• Figure 7.6 b Check 1, Check 2 and Check 4 results for ode45, y3(x) of Lorenz Problem, TOL = 10-6
• Figure 7.7 a Check 1, Check 2 and Check 4 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-5
• Figure 7.7 b Check 1, Check 2 and Check 4 results for ode45, y3(x) of Lorenz Problem, TOL = 10-8
• Figure 7.8 a Check 1, Check 2 and Check 4 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-7
• Figure 7.8 b Check 1, Check 2 and Check 4 results for ode45, y3(x) of Lorenz Problem, TOL = 10-10
• Figure 7.9 a Check 3 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-3
• Figure 7.9 b Check 3 results for ode45, y3(x) of Lorenz Problem, TOL = 10-6
• Figure 7.10 a Check 3 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-5
• Figure 7.10 b Check 3 results for ode45, y3(x) of Lorenz Problem, TOL = 10-8
• Figure 7.11 a Check 3 results for ode45, y2(x) of Predator-Prey Problem, TOL = 10-7
• Figure 7.11 b Check 3 results for ode45, y3(x) of Lorenz Problem, TOL = 10-10