program4 - via step halving only when they exceed their...

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Program 4 Foundations of Computational Math 2 Spring 2011 Due date: 11:59 PM Monday, 4/4/11 Implement an adaptive Newton-Cotes integration strategy and demonstrate its use. Your code: should be based on the composite version of the trapezoidal rule should be able to run in a mode where the step is reFned with step halving over the entire interval and reFnement continues until the estimated error is smaller than a requested tolerance (or a maximum number of points is reached); should be able to run in a mode where the left and right halves of the interval are reFned
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Unformatted text preview: via step halving only when they exceed their alloted portions of the error requested. Use your code to verify the degree of exactness of the method by integrating an appropriate set of poly-nomials; integrate f ( x ) = e x on [ a, b ] = [0 , 2] and compare the true error, I ( f )-I n ( f ), and the error estimate that controls your termination of the adaptive algorithm; compare the number of function evaluations required by the two adaptive forms of Newton Cotes to achieve a similar accuracy over the entire interval of integration. 1...
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