Errors in numerical computation can arise from various sources and can be categorized into different types:

1. Round-off Error: Round-off error occurs due to the finite precision of numerical representations, such as floating-point numbers. When representing real numbers with limited precision, there will always be some discrepancy between the exact mathematical value and its representation. This can lead to accumulation of errors, especially in iterative calculations or when performing numerous arithmetic operations.
2. Truncation Error: Truncation error occurs when an infinite process, such as an infinite series or integral, is approximated by a finite process. For example, when approximating an integral using numerical methods like Simpson’s rule or the trapezoidal rule, the area under the curve is estimated using a finite number of subintervals, leading to truncation error.
3. Discretization Error: Discretization error occurs when continuous problems are approximated by discrete methods. This often happens in numerical simulations, where continuous physical phenomena are represented on a discrete grid. The accuracy of the simulation depends on the resolution of the grid, and errors can arise from approximating continuous quantities at discrete points.
4. Propagation of Error: Errors can propagate through calculations, leading to larger errors in the final result. For example, in numerical algorithms like the numerical solution of differential equations or iterative methods for solving systems of equations, errors from one step can affect subsequent steps, amplifying the overall error.
5. Modeling Error: Modeling error occurs when a mathematical model used in numerical computation does not accurately represent the physical system or phenomenon being studied. This can lead to discrepancies between the numerical results and the actual behavior of the system.
6. Algorithmic Error: Errors can also arise from the choice of algorithm used for numerical computation. Some algorithms may be inherently less accurate or efficient for certain types of problems, leading to errors in the computed results.
7. Human Error: Finally, errors can also stem from mistakes made by the programmer or user, such as coding errors, incorrect input data, or misinterpretation of results.

Mitigating numerical errors often involves employing techniques such as error analysis, using higher precision arithmetic when necessary, refining numerical methods, and validating computational results against known solutions or experimental data. Additionally, careful implementation, rigorous testing, and verification of numerical algorithms can help reduce the impact of errors in numerical computation.