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The Characteristics of the First Kind of Chebyshev Polynomials and its Relationship to the Ordinary Polynomials Maulidi, Ikhsan; Wibowo, Bonno Andri; Apriliani, Vina; Umam, Rofiqul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 2 (2021): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i2.4647

Abstract

In this article, we discuss the Chebyshev Polynomial and its characteristics. The second order difference equation and the process obtaining the explicit solution of the Chebyshev polynomial have been given for each real number. The symmetry and orthogonality of the Chebyshev polynomial has also been demonstrated using the explicit solutions obtained. Furthermore, we have also given how to approx the polynomial function using the Chebyshev polynomials.
Hydrological Assessment and Irrigation Water Optimization Based on Cropping Patterns in the Way Bungur Irrigation Area, Indonesia Putri, Restika; Maula, Frida Yassar; Arif, Muhammad Rizki; Maulidi, Ikhsan; Apriliani, Vina
International Journal of Hydrological and Environmental for Sustainability Vol. 4 No. 3 (2025): International Journal of Hydrological and Environmental for Sustainability
Publisher : CV FOUNDAE

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58524/ijhes.v4i3.926

Abstract

Efficient water management is essential for sustaining agricultural productivity, particularly in regions supported by technical irrigation systems such as the Way Bungur Irrigation Area in Pringsewu Regency, Indonesia. Although water availability in this region is generally adequate, its utilization remains inefficient due to cropping schedules that are not aligned with seasonal hydrological conditions, especially during the dry season. This study evaluates irrigation water requirements based on crop types and the official Cropping Pattern Plan (SK RTT), and compares them with water availability estimated using the F.J. Mock hydrological model. Input data include rainfall records, climatological parameters, river discharge, and field measurements. Crop water requirements were calculated using the FAO Penman–Monteith method, while water availability was assessed through dependable flow analysis. Results indicate that water availability in the Way Bungur watershed generally exceeds irrigation demand across three cropping seasons. However, temporal mismatches between planting schedules and water surplus or deficit periods lead to suboptimal water use. These findings highlight the importance of integrating annual water balance analysis into cropping pattern planning to enhance allocation efficiency, reduce risk, and promote sustainable agricultural development.