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 parabolic 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 parabolic equation is
for all values of x
Q3. The partial differential equation of the temperature in a long thin rod is given by
If α = 0.8 cm^{2}/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an explicit solution at t=0.2 sec is 40.7134°C
40.6882°C 40.6956°C Q4. The partial differential equation of the temperature in a long thin rod is given by
If α = 0.8 cm^{2}/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an implicit solution for t=0.2 sec is 40.7134°C 40.6882°C 40.7033°C 40.6956°C Q5. The partial differential equation of the temperature in a long thin rod is given by
If α = 0.8 cm^{2}/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an CrankNicolson solution for t=0.2 sec is 40.7134°C 40.6882°C 40.7033°C 40.6956°C Q6. The partial differential equation of the temperature in a long thin rod is given by
If α = 0.8 cm^{2}/s, the initial temperature of rod is 40°C, and the rod is divided into three equal segments, the temperature at node 1 (using ∆t=0.1s) by using an explicit solution at t=0.2 s is (For node 0, ), where k=9W/(m°C), h=20W/m^{2}, T_{a}=25°C and T_{0}=(the temperature at node 0) 41.6478°C 38.435°C 39.9983°C 37.5798°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. 
