Conference rusure::math

1246.0. "References on Numerical Solutions to Non-linear PDE?" by GENRAL::HEINTZE () Wed May 23 1990 21:31

    Hmmph...   I just spent a lot of time discovering that numerical
    methods for linear differential equations (specifically the heat
    equation) don't work well for non-linear equations!
    
    The equation I'm trying to solve is essentially the heat equation (a
    linear differential equation)  with  g(x,y,z,t)/c added to the RHS
    making the equation non-linear where g is the amount of heat being
    absorbed by an element and C is the heat capacity of the material.
    
    Can anyone recommend a reference on numerical solutions to non-linear
    differential equations?
    
    Basically the equation is
    
      u[t] = (K/C) (u[xx] + u[yy] + u[zz])  + g(x,y,z,t)/C
    
    where the subscripts denote partial derivatives and K is the thermal
    conductivity and C is the heat capacity and G is the unit power
    delivered to the medium per unit volume.
    
    
                               Thanks,
    
    				Sieg
    

    All methods for nonlinear equations are iterative methods where each
    step of iteration is solving a linear equation.  If it is just a one
    time deal, you could just hack something up on top of your linear
    equation package.  Otherwise, there are packages readily made for this
    kind of thing on the market.
    Eugene

        There are also likely to be free packages available over
        the network.  Look for topics here with titles containing
        LIB or NET or even PAC.
        
        Dan

    It seems to me your PDE IS linear. Nonlinearity in the forcing
    function g(x,y,z,t) does not make the PDE nonlinear.
    (Unless g depends on the solution u or its partials, in which case
    the dependences should be shown explicitly.)

    re -1,
    
    Hmmm..., you are right.
    
    Eugene