The central differencing scheme is a method used to approximate the derivative of a function at a specific point using values of the function at neighboring points. It is derived using Taylor series expansion and has an order of accuracy of 2.
The central differencing scheme is a method used to approximate the derivative of a function at a specific point using values of the function at neighboring points. It is commonly used in numerical methods for solving differential equations or solving other mathematical problems.
To derive the central differencing scheme, we can use Taylor series expansion. The Taylor series for a function at a point x is given by:
f(x + h) = f(x) + hf'(x) + \frac{h^2}{2}f''(x) + O(h^3)
Using the Taylor series expansion of the function at two neighboring points, x + h and x - h, we can derive the central differencing scheme as follows:
f'(x) = \frac{f(x + h) - f(x - h)}{2h} + O(h^2)
This is the central differencing scheme for equidistant numerical resolution.
The order of accuracy of the central differencing scheme is 2, which means that the error of the scheme is proportional to the square of the step size h.