Download presentation

Presentation is loading. Please wait.

Published byDakota Giffen Modified over 3 years ago

1
Solving ODEs with Mathematica Anchors: Scandiumδ Jocelyn Anleitner Diane Feldkamp

2
Mathematica Basics Purpose: Mathematica solves difficult mathematical formulas Focus: solving ordinary differential equations (ODEs) of 1 st and higher order using Mathematica

3
Mathematica Syntax Details about important syntax for Mathematica can be reviewed on the wiki page titled “Solving ODEs with Mathematica” For entering ODEs, use double equal signs (==) to define the functions When finished with a line, use “Shift”+ “Enter” for Mathematica to compute the answer

4
Dsolve and NDSolve For ODEs without initial conditions, use Dsolve For ODEs with initial conditions, use NDSolve Type of EquationSyntaxExample Equation(s)Dsolve for Example One ODEDsolve[eqn,y,x]y''+16y=0Dsolve[y''[x]+16y[x]==0,y,x] Multiple ODEsDsolve[{eqn1,eqn2,…},{y1,y2,…},x] y1'-y2-x=0 y2'-y1-1=0 Dsolve[{y1'[x]-y2[x]-x==0,y2'[x]-y1[x]- 1==0},{y1,y2},x] Type of EquationSyntaxExample Equation(s)Dsolve for Example One ODE NDSolve[{eqn,i1,i2…},y,{x,xmin,xma x}] y''+16y=0,y(0)=1, y'(0)=0 NDSolve[{y''[x]+16y==0,y[0]==1,y'[0]==0},y,{x, 0,30}] Multiple ODEs NDSolve[{eqn1, eqn2,..., i1, i2, …},{y1,y2},{x,xmin,xmax}] y1'-y2-x=0 y2'-y1-1=0 y1(0)=0,y2(0)=0 NDSolve[{y1'[x]-y2[x]-x==0,y2'[x]-y1[x]- 1==0,y1[0]==y2[0]==0},{y1,y2},{x,20}]

5
Example: Semi-batch Reactor (Worked Out Example 2) Reaction: A B First-order ODE with Initial Conditions Use NDSolve in Mathematica Given Variables:

6
Entering in Mathematica Open Mathematica (Version shown here is Mathematica 6) Use the following steps to solve the ODE in Mathematica: 1.Input ODE 2.Define given variables

7
Entering in Mathematica (cont.) 3.Define a variable to NDSolve and enter inputs 4.Plot the solution X is conversion, and X[0] is entered as 0.0001 instead of 0 so that the ODE will not be undefined

8
Sources Solving ODEs with Mathematica (wiki): http://controls.engin.umich.edu/wiki/index.php /Solving_ODEs_with_Mathematica

Similar presentations

OK

SIMULTANEOUS EQUATIONS Problem of the Day! n There are 100 animals in a zoo, some which have 2 legs and some have 4 legs. If there are 262 animal legs.

SIMULTANEOUS EQUATIONS Problem of the Day! n There are 100 animals in a zoo, some which have 2 legs and some have 4 legs. If there are 262 animal legs.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on voice based web browser Ppt on op amp circuits body Ppt on wind power generation Ppt on applied operational research jobs Ppt on job satisfaction and attitude Ppt on acid base titration Ppt on object-oriented programming for dummies Ppt on water resources in hindi Ppt on acid-base titration simulation Ppt on 10 sikh gurus sikhism