-th derivative (and cancels out all other lower and higher-order derivatives up to the desired accuracy), the coefficients must satisfy a system of linear equations:
(The sum of weights for the function value itself must be zero) (Weight for the 1st derivative) (The weight for the -th derivative must be 1) (Higher order terms cancelled for accuracy) This is often represented as a problem: is the vector of unknown weights. 3. Example: Second-Order Forward Difference for Suppose we want to find using three points: Explained: General Finite Difference Stencil (Example) [CFD]
Substitute these expansions into the general summation formula. To ensure the approximation equals the -th derivative (and cancels out all other lower