Final answer:
When the step size is large in numerical solutions for ordinary differential equations, the accuracy of the solution may decrease because fewer data points are being used to approximate the solution.
Step-by-step explanation:
When working through numerical solutions for ordinary differential equations, the step size can have an impact on the accuracy of the solution. If the step size is large, the accuracy of the solution may decrease. This is because a larger step size means that fewer data points are being used to approximate the solution, leading to more error.
For example, if we have an equation y' = f(x, y), where y is the solution we are trying to find as a function of x, using a large step size means that we are taking larger jumps in the x-axis, resulting in less accurate approximations for the value of y at each point.
On the other hand, if we use a smaller step size, we are taking smaller jumps in the x-axis, which means that we are using more data points to approximate the solution. This generally leads to a more accurate solution, although it may take longer to compute.