Final answer:
The question involves using the fourth-order Runge-Kutta method on a differential equation with varying step sizes to study its numerical stability, which is generally better with smaller step sizes.
Step-by-step explanation:
The student's question pertains to solving the differential equation x' = 100(sin(t) - x) with initial condition x(0) = 0 using the fourth-order Runge-Kutta method (RK4) for numerical integration. The task involves implementing the RK4 method at various step sizes h = 0.015, 0.020, 0.025, 0.030 over the interval [0,3] to observe the effects of step size on numerical stability. The RK4 method is a popular and efficient method for solving ordinary differential equations (ODEs) numerically and is particularly known for its balance between accuracy and computational efficiency. However, its numerical stability can be sensitive to the choice of the step size, with smaller steps typically leading to more stable and accurate solutions. By integrating with different step sizes, the student will be able to observe that as the step size increases, the numerical solution may deviate further from the true solution, potentially becoming unstable if the step size is too large.