CL 701: Computational/Numerical Methods . . . Autumn 2009-10 CDEEP - - PowerPoint PPT Presentation

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CL 701: Computational/Numerical Methods . . . Autumn 2009-10 CDEEP - - PowerPoint PPT Presentation

Oct 09, 2022 782 likes •914 views

Slide No: 25a CL 701: Computational/Numerical Methods . . . Autumn 2009-10 CDEEP IIT Bombay Department: Chemical Engineering Instructor: Prof. Santosh K. Gupta E-Mail ID: sk.gupta@che.iitb.ac.in Website Address:

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SLIDE 1

CL 701: Computational/Numerical Methods . . . Autumn 2009-10 Department: Chemical Engineering Instructor: Prof. Santosh K. Gupta E-Mail ID: sk.gupta@che.iitb.ac.in Website Address: http://www.che.iitb.ac.in/faculty/skg.html

Slide No: 25a

CDEEP IIT Bombay

Course Name Lecture No. 25a Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta
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SLIDE 2

Date: 06 Oct 2009 Lecture No.: 25 Lecture Name: STABILITY AND STIFFNESS (CONTINUED) Review: STABILITY: PROPAGATION AND BLOWING-UP OF ROUND-OFF ERRORS Sub-Topics: a) STABILITY (CONTINUED) b) STIFFNESS

CDEEP IIT Bombay

Course Name Lecture No. 25b Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

Slide No: 25b

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SLIDE 3

STABILITY (2ND REASON) || CN:

  • Slide No: 25c

Course Name Lecture No. 25c Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 4

Slide No: 25d Course Name Lecture No. 25d Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

NOTE: BELOW ABSCISSA TOO

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SLIDE 5

Slide No: 25e Course Name Lecture No. 25e Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 6
  • ⁄

⁄

  • ⁄
  • ⁄
  • , , … ,
  • ; : ,
  • Slide No: 25f

Course Name Lecture No. 25f Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 7

WE KNOW , , , , … ,

  • ,

,

  • ,

,

  • Slide No: 25g

Course Name Lecture No. 25g Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 8
  • ;
  • SOLUTION (WITHOUT DERIVATION):
  • Slide No: 25h

Course Name Lecture No. 25h Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 9

OR WE HAD: f MULTIVARIABLE EXPLICIT EULER STABILITY OF MULTIVARIABLE ALGORITHMS (WITHOUT PROOF) || ; , , , … , N EIGENVALUES OF SAME AS FOR SINGLE VARIABLE ALGORITHM

Slide No: 25i Course Name Lecture No. 25i Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

  • cf. FOR

EXPLICIT EULER

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SLIDE 10

EXAMPLES IF

  • ,

IF

  • ,

Slide No: 25j Course Name Lecture No. 25j Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

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SLIDE 11

EXAMPLE: EXPLICIT EULER ASSUME ALL REAL || 2 ALL REAL || 2 FOR STABILITY

  • || , ; ;

Slide No: 25k Course Name Lecture No. 25k Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009)

  • Prof. Santosh K. Gupta

CDEEP IIT Bombay

Re