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Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order
H. Gunawan1, E. Rusyaman2 & L. Ambarwati1,3
1Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia.
2Department of Mathematics, Padjajaran University, Bandung, Indonesia.
3Department of Mathematics, State University of Jakarta, Jakarta, Indonesia
Email: hgunawan@math.itb.ac.id
Abstract. 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(x_i,y_j) = c_{ij}, where 0 < x_1 < ... < x_M < 1, 0 < y_1 < ... є ℝ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.
Keywords: 2-D interpolation; energy-minimizing surfaces
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