Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order
This paper presents a method of finding a continuous, real-valued, function of two variables z = u(x, y) defined on the square S := [0,1]2 , which minimizes an energy integral of fractional order, subject to the condition u(0, y) = u(1, y) = u(x,0) = u(x,1) = 0 and u(xi ,yj)=cð‘–ð‘— , where 0<x1<...<xM,<1, 0<y1<...<yN<1, and cð‘–ð‘— âˆˆ â„ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.
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