When employing a computational method to solve an Ordinary Differential Equation (ODE), the choice of a smaller time step will result in

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BlackTom AI · Accepted Answer

Question restatement: When using a computational method to solve an ODE, choosing a smaller time step generally affects accuracy and cost. 
Option provided: 'Increasd accuracy, and increased coputational cost' (interpreted as 'Increased accuracy, and increased computational cost').
Starting the analysis, it’s important to recall that most time-stepping methods for ODEs (e.g., Euler, Runge-Kutta, multistep methods) have errors that depend on the step size h. For well-behaved problems with a stable method, reducing h tends to reduce the local truncation error, which translates into higher overall solution accuracy. 
Additionally, the total number of steps needed over the integration interval increases as h gets smaller, so the total amount of work (computations, memory accesses) grows roughly inversely with h. This produces a higher computational cost.
Now, evaluating the option piece by piece: 
- 'Increasd accuracy' aligns with the general relationship between smaller step sizes and error reduction in many standard ODE solvers, assuming the method is stable for the problem at hand. This is a plausible and commonly observed outcome. 
- 'increased computational cost' follows from needing more steps to cover the same interval, plus potential overhead from more precise arithmetic if that’s part of the implementation. This is also a typical consequence of a smaller step size. 
Consider potential caveats: if the method is unstable for the chosen step size or the problem stiffness is not handled appropriately, decreasing h could fail to improve or could even worsen accuracy due to instability; in such a case, the statement would not hold. However, for standard non-stiff, well-posed problems with an appropriate method, the trend is clear: smaller h yields better accuracy at the expense of more computation. 
Given the option expresses both increased accuracy and increased computational cost, and these outcomes correctly reflect the standard trade-off in numerical ODE solving, this option is consistent with the typical behavior of many common solvers. 
In summary, the reasoning supports that choosing a smaller time step leads to higher accuracy while also increasing computational cost, making this option correct under common conditions. 
Note on the wording: the option has typographical errors ('Increasd' and 'coputational'), but the intended meaning remains clear and aligns with standard numerical analysis concepts.

BN5206 Re-opened Canvas questions [NON-GRADED, FOR PRACTICE]

When employing a computational method to solve an Ordinary Differential Equation (ODE), the choice of a smaller time step will result in

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