advantage and disadvantage of trapizoidal rule
Answers
Explanation:
The solution is highly accurate for a small order compared to Trapezoidal and Simpson's rule.
It is one step and explicit.
Disadvantages:
It needs the explicit form of derivatives of the function.
Composite Trapezoidal rule:
Advantages:
The method is quite simple in implementing, compared to other methods.
It takes a piecewise linear approximation of the function and hence execution of the solution is faster.
The solution is very rapidly convergent.
It consists of the fact that weighting coefficients are nearly equal to each other.
Disadvantages:
The error is much higher compared to the other methods.
This method is less accurate for non linear functions since it has straight line approximation.
Composite Simpson's rule:
Advantages:
It assumes piecewise quadratic interpolation and hence the accuracy is much higher compared to trapezoidal rule.
It can integrate polynomials up to third order accurately.
The error is less compared to that of trapezoidal rule.
Weighting coefficients are simple and do not fluctuate in terms of magnitude.
Disadvantages:
A large number of ordinates are needed in between the interval.
Romberg Table (Richardson Extrapolation):
Advantages:
Error is reduced subsequently as we go from TK(n) to TK+1(n).
It is efficient in the sense that TK+1(n) is calculated from the already computed values of TK(n) and TK(2n).
The above condition reduces the time and space requirement.
Disadvantages:
In Richardson extrapolation, We are neglecting the higher orders of aih2i.
Corrected Trapezoidal rule:
Advantages:
When integrals of periodic functions are approximated numerically, Corrected Trapezoidal functions are the best choice.
Disadvantages:
This method demands derivatives of the function at the end points of the interval.