Thermodynamics HW Solutions 495

Thermodynamics HW Solutions 495 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction Special Topic: Controlling the Numerical Error 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. The difference between a numerical solution and the exact solution (the error) is primarily due to two sources: The discretization error (also called the truncation or formulation error) which is caused by the approximations used in the formulation of the numerical method, and the round-off error which is caused by the computers' representing a number by using a limited number of significant digits and continuously rounding (or chopping) off the digits it cannot retain. 5-97C The discretization error (also called the truncation or formulation error) 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
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