Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order

Abstract

his 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

Model Regresi Energi Potensial Minimum pada Permukaan Hasil Interpolasi

“…melalui perhitungan yang telah diuraikan pada [2] dan [4] serta menggunakan software sampai iterasi-1225, diperoleh data berupa 20 buah besaran energi minimum yang dihasilkan dari 20 nilai  dengan sebaran antara 1.00 dan 2.00. …”

Application of Reproducing Kernel Hilbert Spaces to a Minimization Problem with Prescribed Nodes

“….) The 1-and 2-dimensional cases have been studied by Gunawan et al [2,3], who show inter alia that the value α > d/2 is a necessary and sufficient condition for the solution to be continuous. As one might expect, the larger the value of α, the smoother the solution.…”