1 / 13

ECE602 BME I Partial Differential Equations in Biomedical Engineering

ECE602 BME I Partial Differential Equations in Biomedical Engineering. Classification of PDEs Initial and Boundary Conditions Numerical solution of PDEs BME Examples. Classification of PDEs. Classification according to order (the highest-order partial derivative present in the equation)

addo
Download Presentation

ECE602 BME I Partial Differential Equations in Biomedical Engineering

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE602 BME I Partial Differential Equations in Biomedical Engineering

  2. Classification of PDEs • Initial and Boundary Conditions • Numerical solution of PDEs • BME Examples

  3. Classification of PDEs • Classification according to • order (the highest-order partial derivative present in the equation) • linearity

  4. elliptic parabolic hyperbolic Classification of PDEs Classification of linear second-order PDEs

  5. Laplace’s equation Heat equation Wave equation Classification of PDEs Examples of linear second-order PDEs elliptic parabolic hyperbolic

  6. Initial and Boundary conditions Diffusion of nutrient across a cell membrane C: the concentration of nutrient D: the diffusivity of nutrient in the membrane

  7. Initial and Boundary conditions Diffusion of nutrient across a cell membrane C: the concentration of nutrient D: the diffusivity of nutrient in the membrane

  8. Initial and Boundary conditions Dirichlet conditions (first kind): the values of the dependent variables are given at fixed values of the independent variables

  9. Initial and Boundary conditions Nuemann conditions (second kind): the derivative of the dependent variables is given as a constant or as a function of the independent variable.

  10. Initial and Boundary conditions Cauchy conditions: a problem that combines both Dirichlet and Neumann conditions

  11. Initial and Boundary conditions Robins conditions: the derivative of the dependent variables is given as a function of the dependent variable itself.

  12. Initial and Boundary conditions • PDE can be classified into • initial-value problem: at least one of the independent variables has an open region • boundary-value problem: the region is closed for all independent variables, and conditions are specified at all boundaries.

  13. Numerical Solutions of PDEs • Finite Difference • Central Difference • Forward Difference • Backward Difference

More Related