I need to compare and contrast Weddle's Rule and Simpson's rule and outline a distinguishing difference between them. I understand Simpson's Rule but I am finding it difficult to obtain clear information about Weddle's rule.
lol! i have the same assignment and im having trouble aswell. I cant find anything on weddles rule on the internet and it is not in my textbook.
hahah same, in every aspect, however go on wolf man for the weddle's rule
To solution is in the idea that Simpson's rule requires an even number of intervals and uses parabola capped trapezoids created by three points. Weddle's rule works accurately for more than 7 and odd numbers of intervals. Good luck in indentifying the derivation of the weird coefficients in the general formula.
To compare and contrast Weddle's Rule and Simpson's Rule, we need to understand their similarities and differences. Both of these numerical integration techniques are used to approximate definite integrals when the exact solution is either difficult or impossible to find analytically.
Simpson's Rule is a numerical method that uses quadratic approximations to estimate the value of the definite integral. It partitions the interval of integration into multiple subintervals and replaces each subinterval with a quadratic interpolation function. The method then calculates the sum of the areas under these quadratic functions to approximate the integral. Simpson's Rule is known for its accuracy, especially when the integrand is relatively smooth.
On the other hand, Weddle's Rule is an extension of Simpson's Rule that uses a higher-degree polynomial approximation. Rather than using quadratic functions, Weddle's Rule utilizes higher-degree polynomials (up to the 10th degree) to estimate the integral. This allows for a more refined approximation over Simpson's Rule, especially when the function being integrated is oscillatory or highly curved.
The key distinguishing difference between Weddle's Rule and Simpson's Rule lies in the complexity of the integration rule. Weddle's Rule is considered more computationally expensive than Simpson's Rule due to the additional terms and calculations required for the higher-degree polynomial approximations. Therefore, while Weddle's Rule may provide a more accurate estimation for certain types of integrands, it might be computationally impractical to use in cases where the gain in accuracy does not outweigh the additional computational effort.
Unfortunately, there is limited information available on Weddle's Rule compared to Simpson's Rule. It is not as widely used or discussed in numerical methods textbooks and resources. Therefore, finding clear and comprehensive information specifically on Weddle's Rule might be challenging.