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Active learning Assignment
Topic : CLASSIFICATION OF SECOND ORDER PARTIAL
DIFFERENTIAL EQUATION
BRANCH : ELECTRICAL ENGINE...
• The general form of a non Homogeneous second order
P.D.E is
• 𝐴 𝑥, 𝑦
𝜕2 𝑢
𝜕𝑥2+B 𝑥, 𝑦
𝜕2 𝑢
𝜕𝑥𝜕𝑦
+C 𝑥, 𝑦
𝜕2 𝑢
𝜕𝑦2+f
𝑥, 𝑦, ...
• EXAMPLE:-1
Classify the Following P.D.E
𝜕𝑢
𝜕𝑡
=
𝜕2 𝑢
𝜕𝑥2
Ans:- Comparing this equation with (1) we get
A=1 , B=0 , C=0
S...
• EXAMPLE:-2
Classify the following P.D.E
𝜕2 𝑢
𝜕𝑥2 +
𝜕2 𝑢
𝜕𝑦2=0
Ans:- Comparing this given P.D.E with (1) we get
A=C=1 , B...
• EXAMPLE:- 3
Classify the Following P.D.E
𝜕2 𝑢
𝜕𝑥2 + 3
𝜕2 𝑢
𝜕𝑥𝜕𝑡
+
𝜕2 𝑢
𝜕𝑡2 =0
Ans:- Comparing this given P.D.E with (1) ...
classification of second order partial differential equation
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classification of second order partial differential equation

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classification of second order partial differential equation

  1. 1. Active learning Assignment Topic : CLASSIFICATION OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATION BRANCH : ELECTRICAL ENGINEERING BATCH : B1 SUBJECT : ADVANCED ENGINEERING MATHEMATICS Prepared By : JIGAR METHANIYA(150120109021) Guided By : Prof. MIHIR SUTHAR 1
  2. 2. • The general form of a non Homogeneous second order P.D.E is • 𝐴 𝑥, 𝑦 𝜕2 𝑢 𝜕𝑥2+B 𝑥, 𝑦 𝜕2 𝑢 𝜕𝑥𝜕𝑦 +C 𝑥, 𝑦 𝜕2 𝑢 𝜕𝑦2+f 𝑥, 𝑦, 𝑢, 𝜕𝑢 𝜕𝑥 , 𝜕𝑢 𝜕𝑦 =F 𝑥, 𝑦 ………..(1) • Equation (1) is said to be • Elliptic , if 𝐵2 -4AC < 0 • Parabolic , if 𝐵2 -4AC = 0 • Hyperbolic , if 𝐵2-4AC > 0 • CLASSIFICATION OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATION
  3. 3. • EXAMPLE:-1 Classify the Following P.D.E 𝜕𝑢 𝜕𝑡 = 𝜕2 𝑢 𝜕𝑥2 Ans:- Comparing this equation with (1) we get A=1 , B=0 , C=0 So , 𝐵2 -4AC = 0 Hence given P.D.E. is parabolic.
  4. 4. • EXAMPLE:-2 Classify the following P.D.E 𝜕2 𝑢 𝜕𝑥2 + 𝜕2 𝑢 𝜕𝑦2=0 Ans:- Comparing this given P.D.E with (1) we get A=C=1 , B=0 So , 𝐵2-4AC = -4<0 Hence , given P.D.E is elliptic.
  5. 5. • EXAMPLE:- 3 Classify the Following P.D.E 𝜕2 𝑢 𝜕𝑥2 + 3 𝜕2 𝑢 𝜕𝑥𝜕𝑡 + 𝜕2 𝑢 𝜕𝑡2 =0 Ans:- Comparing this given P.D.E with (1) we get A=1 , B=3 , C=1 So , 𝐵2 -4AC = 9-4 = 5>0 Hence the given P.D.E is hyperbolic.

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