To derive the central differencing scheme for equidistant numerical resolution using Taylor series, we can use the central difference formula to approximate the first derivative. The order of accuracy of the central differencing scheme is 2, which means that the error of the scheme is proportional to h^2.
To derive the central differencing scheme for equidistant numerical resolution using Taylor series, we can start by considering the Taylor series expansion of a function f(x) around a point x0:
f(x) = f(x0) + (x - x0)f'(x0) + ½(x - x0)^2f''(x0) + …
To obtain the central difference scheme, we can approximate the first derivative f'(x0) using the central difference formula:
f'(x0) = (f(x0 + h) - f(x0 - h)) / (2h)
The order of accuracy of the central differencing scheme is 2, which means that the error of the scheme is proportional to h^2.