Numerical Differentiation
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Numerical differentiation is a technique of numerical analysis to produce an estimate of the derivative of a mathematical function or function subroutine using values from the function and perhaps other knowledge about the function.
The discretization method is called finite differences based on the following equation:
which finally can be expressed as the central difference scheme:
Links:
en.wikipedia.org/wiki/Numerical_differentiation
Tasks
- L1: Create a data structure, e.g., an array, which stores simple x coordinates and another double value.
- L1: Write the function
on all elements of the container. - L1: Detect the boundary elements of the container.
- L2: Determine a formula for numerical differentiation with the finite difference method and implement a function for the first derivation.
- L2: Implement the formula for the boundary regions.
- L3: Implement the 2nd derivate by using the Taylor-series, this is a 5-point approximation.