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Math Help - solving partial differential equations using complex numbers

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    8

    solving partial differential equations using complex numbers

    hi there folks,

    what i wanted to ask today is the following :

    i know that complex numbers can be used to simple differential equations of the second order such as 10y''+y'+1=0

    my question is this , lets take a partial differential equation such as the wave equation (for those not familiar )

    now , given the proper initial values , or an adequate set of boundary limits i can guess a solution , quantimize(spelling?) it and find a soltuion for the equation dependant on n,x,t
    my question is the following , i know that some people will prefer to solve such an equation using complex numbers, so my request is this , could someone provide an example to doing so ? any partial differential equation will do , i only gave the wave equation as an example.
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  2. #2
    Junior Member
    Joined
    Jan 2009
    Posts
    56
    Usually these equations are solved by letting u(x,t)=Aexp(i(kx-wt)).

    Every class of equations has its own method of solving it.
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