 Numerical Integration Overview

Subject Mathematics Numerical Analysis

Question

The first part of the paper needs to have an introduction that sells why your problem is important to you. The second part of the paper is your mathematical approach. There needs to be two methods used and why these two were picked.

The stuff we covered in this class were round off error, convergence, bisection method, fixed point iteration, Newton's Method, the Secant Method, accelerating convergence, interpolation and lagrange polynomial, Neville's method, divided differences, hermite interpolation, numerical differentiation and the 3 point formulas, richardson extrapolation, numerical integration, Romberg integration, and linear systems of equations.

The third part of the paper are your results. The math results and non math results, matlab code, and graphs of which method was better.

The powerpoint is just an overview of the project that should be around a 5 minute presentation. There is not limit to the length of the paper.

Solution Preview

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What is numerical integration?
In numerical analysis, numerical integration is a process of approximating definite integrals or finding the area under the curve by using various numerical integrating methods namely, trapezoidal, Simpson, quadrature. But here we are only considering trapezoidal and Simpson method and composite integration methods (Simpson, trapezoidal) for integration. Sometimes it is difficult to solve the definite integral of any function f(x) which is continuous on the interval [a,b] but whose antiderivative i.e., F(x) is not known, by Newton-Leibnitz formula( general integration method) which is defined as: ∫ᵇₐ f(x)=F(a)-F(b)
Then we use numerical integration methods for such f(x) (an example of such f(x) is f(x) =exp⁡(-x²), its antiderivative cannot be found by elementary means)....

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