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

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: http://www.che.iitb.ac.in/faculty/skg.html Course Name Lecture No. 25a Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25b Date: 06 Oct 2009 CDEEP IIT Bombay 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 Course Name Lecture No. 25b Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

STABILITY (2 ND REASON) |� � | � � Slide No: 25c CDEEP IIT Bombay ��� ��� ����� � � � � ��� � � CN: � ��� � � � � � � � Course Name Lecture No. 25c Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25d CDEEP IIT Bombay NOTE: BELOW ABSCISSA TOO Course Name Lecture No. 25d Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25e CDEEP IIT Bombay Course Name Lecture No. 25e Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25f �� � �� � , � � , … , � � � ⁄ ��� � �� � � � � ��� ⁄ �� � �� � � � � CDEEP � � � � IIT Bombay � � � � � � � ��� ⁄ �� � �� � � � � � � � � � � ⁄ � �� � �� � � � ��� � � � � �� � � � � � ; ��: � � �, � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � �� � � � � � � � Course Name Lecture No. 25f Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25g CDEEP IIT Bombay WE KNOW �� � , � � � � �,� � � � �� � � � � �� � , � � , … , � � � � � � �� � � � �� � �� � � � �,� � � � � �� � � � �� � � � �,� � �� � �� � � � ,� � � � ,� � �������� Course Name Lecture No. 25g Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25h �� ��� � � � � �� � � � � � � � � ; � � � � CDEEP �� IIT Bombay SOLUTION (WITHOUT DERIVATION) : ���� � � �� � �� � � � � �� � � � � � � �� � � � � ��� � � �� � �� � � � � �� � � � � � � �� � � � �� � � � � �� � �� � � � �� � � � � ��� � � � �� �� � � � � �� � � � ��� � � � � � � Course Name Lecture No. 25h Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

Slide No: 25i OR � ��� � � � � � �� � � � � � � � cf. FOR �� �� � ���� CDEEP IIT Bombay WE HAD: f �� � � � � � � � � � � EXPLICIT EULER � ��� � � � � ���� � � � � ��� � � � � �� �� � � � MULTIVARIABLE EXPLICIT EULER STABILITY OF MULTIVARIABLE ALGORITHMS (WITHOUT PROOF) |� � ��� � �| � �; � � �, �, �, … , � � � N EIGENVALUES OF � � � � SAME AS FOR SINGLE VARIABLE ALGORITHM Course Name Lecture No. 25i Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

EXAMPLES Slide No: 25j IF � ��� � ��� � �� � �� � � �� � CDEEP IIT Bombay � ��� � �� � �� � � � , � � ��� ��������� �� � � �� � � �� IF � ��� � ��� � � � �� � � �� � �� � � � � ��� � ��� � �� � � � ��� � � �� � � � � , � � ��������� �� � �� � Course Name Lecture No. 25j Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta

EXAMPLE: EXPLICIT EULER Slide No: 25k ASSUME � � ALL REAL CDEEP IIT Bombay Re ���� �|� � | � 2 ALL � � REAL �|� � | ��� � 2 FOR STABILITY � � � |� � | ��� ���� �, � ; � � � � � � ; � � � � � Course Name Lecture No. 25k Instructor’s Name CL 701 Computational Methods in Chemical Engineering (06 Oct 2009) Prof. Santosh K. Gupta