CH ENGR 104C Lecture Notes - Lecture 5: Discretization Error, Round-Off Error, Finite Difference Method

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5-96c the results obtained using a numerical method differ from the exact results obtained analytically because the results obtained by a numerical method are approximate. 5-97c the discretizationerror(also called the truncationor formulationerror) is due to replacing the derivatives by differences in each step, or replacing the actual temperature distribution between two adjacent nodes by a straight line segment. The difference between the two solutions at each time step is called the local discretizationerror. The total discretization error at any step is called the globalor accumulated discretization error. The local and global discretization errors are identical for the first time step. 5-98c yes, the global (accumulated) discretization error be less than the local error during a step. The global discretization error usually increases with increasing number of steps, but the opposite may occur when the solution function changes direction frequently, giving rise to local discretization errors of opposite signs which tend to cancel each other.

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