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Numerical Solution: Ordinary & Partial Differential Equation
Rating: 4.4 out of 5(76 ratings)
666 students

Numerical Solution: Ordinary & Partial Differential Equation

Introductory numerical methods to solve ordinary and partial differential equations. Fortran; Python codes.
Created byRobert Spall
Last updated 12/2023
English

What you'll learn

  • Basic numerical solution techniques for solving ordinary and partial differential equations.

Course content

6 sections39 lectures2h 11m total length
  • Introductory Material3:51

    Students will see some practical applications of numerical methods.

  • Classification of differential equations.

Requirements

  • Beginning calculus, differential equations, and programming experience.

Description

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

Who this course is for:

  • STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations.