Q1. In a general second order linear partial differential equation with two independent variables,
where A , B , C are functions of x and y, and D is a function of x , y , , , then the PDE is elliptic if B^{2}4AC<0 B^{2}4AC>0 B^{2}4AC=0 B^{2}4AC≠0 Q2. The region in which the following equation
acts as an elliptic equation is
for all values of x
Q3. The finite difference approximation of in the elliptic equation
at (x,y) can be approximated as
Q4. Find the temperature at the interior node given in the following figure using the direct method 45.19 °C 48.64 °C 50.00 °C 56.79 °C Q5. Find the temperature at the interior node given in the following figure
Using the Lieberman method and relaxation factor of 1.2, the temperature at x=3, y=6 estimated after 2 iterations is (use the temperature of interior nodes as 50°C for the initial guess) 52.36 °C 53.57 °C 56.20 °C 58.64 °C Q6. Find the steadystate temperature at the interior node as given in the following figure
53.57 °C 66.40 °C 68.20 °C 69.59 °C

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 336205350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624, 0836981, 0836916, 0836805, 1322586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Other sponsors include Maple, MathCAD, USF, FAMU and MSOE. Based on a work at http://mathforcollege.com/nm. Holistic Numerical Methods licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. 
