Education 2

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INTRODUCTION

alt — Figure 4: Plotting *E-1* versus time step for the unperturbed pendulum. The initial conditions are *q₀ = π/2, p₀ = 0*, and we have calculated 600 time steps each of size *.02*. If the calculation conserved energy perfectly, E would be exactly one.

a. Third-order Runge-Kutta.

b. Fourth-order Runge-Kutta.

c. Symplectic algorithm (fourth-order accurate).