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How easily can we extend the numerical integration methods discussed to partial differential equations? How useful would that be in graphics/animation?


How do we account for the errors in replacing accurate functions with samples?


To make the calculated value of the new configuration more concise, we might need to use very small time steps. But in real implementation, the calculation of small float values might lead to loss of precision. Is there a good solution to the problem?


How can we calculate the error here in the formula? Are there some ways to reduce it? Random sampling, monte carlo?


are we essentially approximating a continuous model in discrete time?


Is monte carlo a popular way to reduce the error?