Applied numerical methods 2

Content of the material: Numerical Methods

Chapter 1: Simple and Multiple Numerical Integration.

I.1 Trapezoid method.

I.2 Simpson's method.

I.3 Gaussian quadrature method.

Chapter II: Analytical solution of ordinary differential equations.

II.1 first order of ordinary differential equations

II.2 second order of ordinary differential equations

Chapter III: Numerical solution of ordinary differential equations (Cauchy problem)

III.1 Cauchy's problem

III.2 Euler's method

III.3 Taylor's method

III.4 Range-Kutta method of order 2

III.5 Differential equations of order greater than 1 and a system of differential equations.

Chapter IV: Numerical Solution of Ordinary Differential Equations (Dirichlet's Problem)

IV.1. Finite difference method.

IV.2 Rayleigh-ritz method

IV.3 Tir Method.