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partial differential equations

partial differential equations

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  • MRCE, B.Tech ECE 1st year
  • MRCE, B.Tech ECE 1st year
  • Transcript

    • 1. APPLICATION OF PARTIAL DIFFERENTIAL EQUATIONS
      • Presented By:
      • Rahul Sharma
      • Ravinder
      • Tamesh
      • Tejaasvi Bhogra
      MRCE, B.Tech ECE 1st year
    • 2. INTRODUCTION
      • These equations are usually classified according to their mathematical form.
      • Differential equations involving two or more independent variables are called partial differential equations.
      • These equations may have only boundary conditions, in which they are referred to as Boundary Value Problems (BVP) or steady-state equations.
      MRCE, B.Tech ECE 1st year
    • 3. CLASSIFICATION
      • Wave Equation :
      • 1-D Heat flow :
      • 2-D Heat flow:
      • Radio Equations:
      MRCE, B.Tech ECE 1st year
    • 4. Methods of Separation Of Variables
      • Assumption
      • Dependent Variable is the product of 2 functions, each involving only one of the independent Variables.
      • Outcome : 2 Ordinary Differential Equations are Formed.
      MRCE, B.Tech ECE 1st year
    • 5. Equation of Vibrating String OR 1D Wave Equation
      • The boundary conditions to be satisfied by the Equation are :
      • y=0 ,when x=0
      • Y=0 , when x =1
      • [ These should be satisfied by every value of ‘t’ ]
      MRCE, B.Tech ECE 1st year
    • 6. 1 Dimensional Heat Flow = K/= K/s ρ which is known as Diffusivity of the material of the bar . Where , S = specific Heat ρ = density of material & K = Conductivity. MRCE, B.Tech ECE 1st year
    • 7. SOLUTION OF THE HEAT EQUATION MRCE, B.Tech ECE 1st year
    • 8. 2 D Heat Flow
      • Note 1 : in the steady state,u is independent of t,so that du/dt = 0
      • d2u/dx2 + d2u/dy2 = 0
      • Which is Laplace’s Equation in 2-D
      MRCE, B.Tech ECE 1st year
    • 9. 2-D Heat Flow
      • (d2u/dx2 + d2u/dy2 +d2u/dz2 ) = du/dt
      • In Steady state,it reduces to
      • (d2u/dx2 + d2u/dy2 +d2u/dz2 ) = 0
      • Which is Laplace’s Equation in 3-D
      MRCE, B.Tech ECE 1st year
    • 10. Solution Of Laplace’s Equation in 2D MRCE, B.Tech ECE 1st year
    • 11. THANK YOU MRCE, B.Tech ECE 1st year

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