Chapter 10.02 Parabolic Partial Differential Equations

Chapter Parabolic Partial Differential Equations After reading this Chapter , you should be able to: 1. Use numerical methods to solve Parabolic Partial Differential Equations by explicit, implicit, and Crank- nicolson methods. The general second order linear PDE with two independent variables and one dependent variable is given by 022222=+ + + DyuCyxuBxuA (1) where CBA,,are functions of the independent variables, x ,y, and D can be a function of xuuyx ,,, and yu . If 042= ACB, Equation (1) is called a Parabolic Partial Differential equation. One of the simple examples of a Parabolic PDE is the heat-conduction equation for a metal rod (Figure 1) tTxT = 22 (2) where =T temperature as a function of location, x and time, t in which the thermal diffusivity, is given by Ck = where =kthermal conductivity of r

implicit, and Crank-Nicolson methods. The general second order linear PDE with two independent variables and one dependent variable is given by . 0. 2 2 2 2 2 + = ∂ ∂ + ∂ ∂ ∂ + D y u C x y u B x A (1) where . A,B, C. are functions of the independent variables, x, y, and . D. can be a function of . x u x y u. ∂ ∂, , , and . y u ...

Tags:

  Cranks, Parabolics, Nicolson

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