Local truncation error refers to the error made in a single step of a numerical method when approximating a mathematical function. This error arises because numerical methods, like Runge-Kutta, use finite approximations for derivatives, which leads to discrepancies between the true solution and the computed value. Understanding local truncation error is crucial for analyzing the overall accuracy and stability of numerical algorithms, as it directly impacts the convergence behavior and reliability of results obtained through these methods.
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