chapter5.page05

chapter5.page05 - tMesh(a, b, N) to compute the ending of...

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2. EULER’S METHOD 5 2.2. Mathcad implementation of Euler’s Method. First, we have the following simple algorithm for the Euler’s method, Input f , a , b , x 0 n. Output: the approximate solution to x 0 = f ( t,x ) with initial guess x 0 over interval [a, b]. Step One: Initialization Set h = b - a n Set x 0 = x 0 Set t 0 = a Step Two: For i=1 to n do Step Three Step Three: Set x i = x i - 1 - f ( t i - 1 ,x i - 1 ) * h Set t i = t i - 1 + h Step Four return x. Notice, algorithm return an array of values, the ith element of the return array is an approximations of x ( t ) at t = a + ih. The following screen shot shows Mathcad code for implementing the algorithm. Notice, we also create a function
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Unformatted text preview: tMesh(a, b, N) to compute the ending of subinterval for graphing purpose. Figure 3. Mathcad code for Eulers Method Notice the line to line corresponding between the Mathcad and the algorithm. Since Mathcad programming language is a scripting lan-guage, the translation between algorithm and code is straight forward, and you dont need to worry about the variable type, io, etc. Also, without explicit return statement, the result of last is, by default, will be returned....
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