numerical methods odes

numerical methods odes - Notes - Numerical Methods...

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Notes - Numerical Methods Numerical methods for simulation and data analysis are widely used in both systems and synthetic biology. In this part of the course you will investigate three different numerical methods: 1 . Solving Differential Equations 2. Solving nonlinear equations 3. Fitting data to models Methods for solving stochastic models will be dealt with in a separate assignment. 1. Basic Concepts in Numerical Analysis All numerical methods involve approximations due to either limits in the algorithm or physical limits in the computer hardware. Errors associated with measurements or calculations can be characterized with reference to accuracy and precision . Accuracy refers to how closely a computed or measured value agree with the true value. Precision refers to how close measured or computed values agree with each other after repeated sampling. Nether Precise NOR accurate: Precise, but NOT accurate: Accurate but NOT precise: Precise AND accurate
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Simple Error Definitions There are a number of ways to describe errors in measurements and calculations. The simplest is the absolute error , this is the difference between the measured or calculated value and the true value. A shortcoming of the absolute error is that it doesn t take into account the order of magnitude of the value under consideration. One way to account for the magnitude is to consider instead the relative error . Many numerical methods are interative, that is they involve repeating the same calculation many times. In terms of error analysis, two types of error emerge, local and global errors. The local error is the error introduced during one operation of the iterative process. The global error is the accumulative error over many iterations. Note that the global error is not simply the sum of the local errors due to the nonlinear
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numerical methods odes - Notes - Numerical Methods...

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