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One of the substantial advantages of LabVIEW's G Math Toolkit is the ability to admit measured values as parameters of differential equation models and to feed back the results of these calculations to the process by means of digital-to-analog conversion or other interfaces. Thus, if you're investigating differential equations, you could very well get specific parameters directly from process measurements, and the results could also have a feedback effect on the process through digital-to-analog conversion or other actuators. These features far surpass the performance of other mathematics and simulation packages. |
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A Numerical Experiment:
Newton-Raphson Method |
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For many reasons, LabVIEW is well suited for carrying out numerical investigations. The three most important arguments are: |
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· You can describe many algorithms in numerical analysis quite well by using a data flow machine in conjunction with graphical orientation. |
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· The user interface allows you to react quickly to new situations, so you can easily visualize each auxiliary variable. This leaves room for you to experiment and study new phenomena. |
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· As a rule, you can use simple wiring or branching of existing structures on the programming side, which helps you achieve the preceding argument. |
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The Newton-Raphson method is a good example of a numerical investigation. You can use this method to determine zeros of a given function f(x) by using the derivative of this function. For practical reasons, the Newton-Raphson method succeeds because it has good convergence properties, and you can use this method for both 1-D or n-D real-valued functions as well as 1-D or n-D complex-valued functions. |
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The fundamental idea of the method is based on the approximation formula (only the 1-D case is shown here): |
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from which it follows, after transformation, that |
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