Using Simpson's Rule to estimate the area of the circle (4), c (1, 0)with(n=4).

Answered: Using Simpson s Rule to estimate the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Using Simpson's Rule to estimate the area of the circle (4), c (1, 0)with
(n=4).

Expert Solution

Step 1

Mathematical methods used to solve equations or evaluate integrals or solve differential equations can be classified broadly into two types.

Analytical Methods
Numerical Methods

Analytical methods are those which by an analysis of the equation obtain a solution directly as a readymade formula in terms of say, the coefficients present in the equations.

In numerical solution, instead of directly writing the answer in terms of some formula, we perform stepwise calculations using some algorithms or numerical procedures and arrive at the same results.

The advantage of numerical methods is that usually, these procedures work on a much wider range of problems as compared to analytical solutions which work in a limited class of problems.