Numerical Integration: Composite Midpoint Method and Error

Derive the composite midpoint method and composite error.

Must be done on Excel - two problems

Solve the following initial value problem by Euler's method using h = 0.1. Find an error by comparing to exact solution. Then solve it by the Runge-Kutta method. Find an error. dy/dx = 3xy²; y(0) = 1; 0 ≤ x ≤ 1

Rootfinding for Nonlinear Equations: Newtion's Method

See attachment!

Rootfinding for Nonlinear Equations

19. Show that ... See attachment!

Rootfinding for Nonlinear Equations

See attachment!

Rootfinding for Nonlinear Equations: Newtion's Method

See attachment!

Numerical Solution of Systems of Linear Equations: Gaussion Elimination

See attachement!

Numerical Solution of Systems of Linear Equations: Computing Matrices

See attachment!

Numerical Solution of Systems of Linear Equations: Choleski Method

See attachment!

from the book. ELEMENTARY NUMERICAL ANALYSIS by ATKINSON. HAN

8.(a) As another approximation to I(f) = integrand from a to b f(x)dx, replace f(x) by the constant f[(a+b)/2] on the entire interval a ≤ x ≤ b. Show that this leads to the numerical integration formula M1( f ) = (b-a) f((a+b) / 2),. graphically illustrate this approximation. (b)In anology with the derivation ...continues