Feasibility Study of Hydro Power Plant (HPP) Lubuak Gadang Sangir South Solok

The feasibility study is one of the principal documents in building a hydropower plant consisting of technical, economic, and financial aspects. Contained technical studies on civil, mechanical, and electrical. This requires data on hydrologic, geology, land contours, river discharge, water catchment areas, and so on. Economic and financial studies include cost and financial parameters such as; BEP, IRR, NVP, BCR, and others. The installed capacity of a hydropower plant is given in optimization based on the Flow Duration Curve (FDC) and the Capacity Factor (CF) used the Newton Interpolation Method. The results showed that the installed power capacity was 11.99 MW. The water discharge was 31.603 m3/secs and the effective head was 37.5 meters. Annual income is around IDR 103.026 billion. Finally, HPP Lubuak Gadang is technically, economically, and financially feasible, so it is feasible to carry out the next process.

Numerical Solution of a Certain Class of Singular Fredholm Integral Equations of the First Kind via the Vandermonde Matrix

In this paper, a computational method is presented to solve potential-type Fredholm integral equations of the first kind, equations in which the unknown functions are singular at the endpoints of the integration domain, in addition to the weakly singular logarithmic kernels. This method provides a numerical solution based on the Newton interpolation technique via the Vandermonde matrix, which can accommodate an approximation of the unknown function, in such a manner that its singularity is easily removed, as well as the removal of kernel singularity. In addition, the Gauss–Legendre formula is adapted and applied for the computations of the obtained convergent integrals. Thus, the obtained numerical solution is equivalent to the solution of an algebraic equation in matrix form without applying the collocation method. The numerical solutions of the illustrated example are strongly converging to the exact solution for all values of 1 x  including the end-points 1 whereas the exact solution fails to find the functional values at these end-points; which ensures the powerful and high accuracy of the presented computational technique

IN INTERPOLATING THE VALUES OF FUNCTIONS SPECIFIED BY THE TABLE EFFECTIVENESS OF THE LEAST SQUARES METHOD

The article provides a general algorithm of the method of least squares (OLS) for the compilation of a program account, taking into account the features of the Gram matrix. In fact, the difference and advantage of the OLS from the long-known Langrange and Newton interpolation polynomials is emphasized. Using the general MNC algorithm, the square version of the MNC is considered. The characteristic of the full algorithm of the square version is given using special selected mathematical formulas. The scope of OLS in household and practical computational problems is indicated. The application of the least squares method has a wide range, especially for geographical forecasts, hydrometeorological control, and dosage of geological resources. Therefore, for applied calculations, DVI is used for more accurate calculation of approximate values of functions that are suitable in some values and are presented in the form of tables. Its main idea is to create a function and correct deviations caused by errors made during measurement.