Difference Equations from Differential Equations

1. Front Matter

   Pages N1-X

   PDF

2. Ordinary Differential Equations

   • Wilbert James Lick

   Pages 1-72

3. Parabolic Equations

   • Wilbert James Lick

   Pages 73-126

4. Hyperbolic Equations

   • Wilbert James Lick

   Pages 127-191

5. Elliptic Equations

   • Wilbert James Lick

   Pages 192-218

6. Applications

   • Wilbert James Lick

   Pages 219-272

7. Back Matter

   Pages 273-287

   PDF

In computational mechanics, the first and quite often the most difficult part of a problem is the correct formulation of the problem. This is usually done in terms of differential equations. Once this formulation is accomplished, the translation of the governing differential equations into accurate, stable, and physically realistic difference equations can be a formidable task. By comparison, the numerical evaluation of these difference equations in order to obtain a solution is usually much simpler. The present notes are primarily concerned with the second task, that of deriving accurate, stable, and physically realistic difference equations from the governing differential equations. Procedures for the numerical evaluation of these difference equations are also presented. In later applications, the physical formulation of the problem and the properties of the numerical solution, especially as they are related to the numerical approximations inherent in the solution, are discussed. There are numerous ways to form difference equations from differential equations.

• Algebra
• algorithm
• algorithms
• hyperbolic equation
• linear algebra
• numerical methods
• partial differential equation
• water quality and water pollution
• air pollution and air quality

• Dept. of Mechanical and Environmental Engineering, University of California, Santa Barbara, USA

  Wilbert James Lick

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