Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order

H. Gunawan (Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia.)
E. Rusyaman (Department of Mathematics, Padjajaran University, Bandung, Indonesia.)
L. Ambarwati (Department of Mathematics, State University of Jakarta, Jakarta, Indonesia)

Journal of Mathematical and Fundamental Sciences
Vol. 43 No. 3 (2011)

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)=c𝑖𝑗 , where 0<x1<...<xM,<1, 0<y1<...<yN<1, and c𝑖𝑗 ∈ ℝ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.