车南种彩头寻 Numerical Differentiation
Numerical Differentiation
Numerical Differentiation Estimate the derivatives (slope,curvature,etc.) of a function by using the function values at only a set of discrete points Ordinary differential equation (ODE) Partial differential equation (PDE) Represent the function by Taylor polynomials or Lagrange interpolation Evaluate the derivatives of the interpolation polynomial at selected nodal points
Numerical Differentiation ◼ Estimate the derivatives (slope, curvature, etc.) of a function by using the function values at only a set of discrete points ◼ Ordinary differential equation (ODE) ◼ Partial differential equation (PDE) ◼ Represent the function by Taylor polynomials or Lagrange interpolation ◼ Evaluate the derivatives of the interpolation polynomial at selected nodal points
True derivative Approximation Numerical Differentiation Forward difference (a) Backward difference True derivative Centered difference Approximation 2
Forward difference Backward difference Centered difference Numerical Differentiation
Forward difference True derivative Approximation Xi-1 Xi X+1
Forward difference xi−1 xi xi+1 x h
Backward difference True derivative Approximation Xi-1 xi Xi+1
Backward difference xi−1 xi xi+1 x h