Numerical Solution: Ordinary & Partial Differential Equation

Numerical Solution: Ordinary & Partial Differential Equation free download

Introductory numerical methods to solve ordinary and partial differential equations. Fortran; Python codes.

The course provides an introduction to the numerical solution of ordinary and partial differential equations and is at a level appropriate for undergraduate-level STEM students.  Prior knowledge of numerical methods is helpful but not necessary as (most) prerequisite material is introduced on an as-needed basis.  Knowledge of a scientific programming language is necessary for those wishing to write their own codes.  All codes used to demonstrate methods and solve example problems (primarily in both Fortran and Python) are available for downloading, as are the class notes.  For the ordinary differential equations, we will study numerical techniques to solve:

1) Initial value (or propagation) problems

2) Boundary value (or equilibrium) problems

3) Eigenvalue (or characteristic value) problems

In terms of partial differential equations, we will concentrate on finite-difference approaches to solve second-order partial differential equations.

These equations may be classified as elliptic, parabolic, or hyperbolic. The classification helps determine the best approach to obtain a numerical solution.  We will focus on elliptic and parabolic partial differential equations.

The primary course sections are:

SECTION 2: ODE’s: INITIAL VALUE PROBLEMS

SECTION 3: ODE’s: BOUNDARY VALUE PROBLEMS

SECTION 4: ODE’s: EIGENVALUE PROBLEMS

SECTION 5: ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

SECTION 6: PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS