project numerical solutions to ordinary differential equations in hardware
Download
Skip this Video
Download Presentation
Project: Numerical Solutions to Ordinary Differential Equations in Hardware

Loading in 2 Seconds...

play fullscreen
1 / 14

Project: Numerical Solutions to Ordinary Differential Equations in Hardware - PowerPoint PPT Presentation


  • 134 Views
  • Uploaded on

Project: Numerical Solutions to Ordinary Differential Equations in Hardware. Joseph Schneider EE 800 March 30, 2010. Ordinary Differential Equations. Function with one independent variable and derivatives of the dependent variable Eg . y’ = 1 + y/x

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Project: Numerical Solutions to Ordinary Differential Equations in Hardware' - lotte


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
project numerical solutions to ordinary differential equations in hardware

Project: Numerical Solutions to Ordinary Differential Equations in Hardware

Joseph Schneider

EE 800

March 30, 2010

ordinary differential equations
Ordinary Differential Equations
  • Function with one independent variable and derivatives of the dependent variable
  • Eg. y’ = 1 + y/x
  • Requires some initial condition in order to be solved
  • Eg. y(1) = 2
ordinary differential equations1
Ordinary Differential Equations
  • Found in many areas of engineering
  • Radioactive decay, heat equation, motion…
  • In electrical engineering, charge, flux, voltage, current, all intertwined by differential equations
ordinary differential equations2
Ordinary Differential Equations
  • In some cases, original equation can be derived with relative ease; Exact solutions are then available
  • In other cases, we will only have the ODE to work with
  • Numerical solutions have been developed to deal with these cases
ordinary differential equations3
Ordinary Differential Equations
  • Most basic case: Euler’s Method
  • Selecting a step size h, iterate from initial value to desired value using the derivative function
ordinary differential equation
Ordinary Differential Equation
  • Euler’s Method most basic case – Simple, but inaccurate
  • Variety of other methods that have been developed
ordinary differential equations6
Ordinary Differential Equations
  • Error directly linked with step size
  • As step size decreases, error decreases; However, takes longer for process to complete
  • Implemented in software (eg. Matlab), more accurate methods take several seconds to complete for smaller scale cases; Several minutes for larger cases
ordinary differential equations7
Ordinary Differential Equations
  • Original project goal: Implement the Runge-Kutta 4th order method in hardware for improved speed
project
Project
  • Euler’s method also implemented for comparisons on area, timing, and accuracy.
  • Current implementation: Uses fixed-point number representation, state machine
  • Further steps on this implementation
    • Variable-point number representation to improve accuracy
    • Modify for parallelism to examine impacts on area, timing
project1
Project
  • Second implementation: Error-controlled design of Runge-Kutta method
  • Error is specified at beginning of process, step size is varied to ensure final result meets error specifications
project2
Project
  • For second implementation, desired to use a hardware design to improve on bottleneck of software design
  • Comparisons to software on time vs. error threshold
ad