hw11 - Problem 11.2 Consider the Runge Kutta method called...

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Homework 11 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Wednesday, 4/20/11 Problem 11.1 Consider the Runge Kutta method called the implicit midpoint rule given by: ˆ y 1 = y n - 1 + h 2 f 1 f 1 = f ( t n - 1 + h 2 , ˆ y 1 ) y n = y n - 1 + hf 1 An alternate form of the the method is given by: y n = y n - 1 + hf ( t n + t n - 1 2 , y n + y n - 1 2 ) Show that the two forms are identical.
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Unformatted text preview: Problem 11.2 Consider the Runge Kutta method called the explicit trapezoidal rule given by: y 1 = y n-1 + hf ( t n-1 , y n-1 ) y n = y n-1 + h 2 ( f ( t n-1 , y n-1 ) + f ( t n , y 1 ) ) Show that the method has truncation error O ( h 2 ). 1...
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