{"id":4885,"date":"2021-08-02T15:01:55","date_gmt":"2021-08-02T08:01:55","guid":{"rendered":"https:\/\/istiarto.staff.ugm.ac.id\/?page_id=4885"},"modified":"2026-02-08T19:31:35","modified_gmt":"2026-02-08T12:31:35","slug":"solusi-numerik-persamaan-diferensial","status":"publish","type":"page","link":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/kuliah\/sarjana-s1\/solusi-numerik-persamaan-diferensial\/","title":{"rendered":"Solusi Numerik Persamaan Diferensial"},"content":{"rendered":"\r\n

Mata kuliah “Solusi Numerik Persamaan Diferensial” merupakan salah satu mata kuliah wajib di Program Sarjana DTSL FT UGM, Semester V, 2 sks. Kuliah diselenggarakan dalam 14\u00d7100′ tatap muka, dibagi menjadi dua bagian, masing-masing 7\u00d7100′ tatap muka. Bagian I berlangsung sebelum UTS dan Bagian II berlangsung sesudah UTS.<\/p>\r\n\r\n\r\n\r\n

Materi Kuliah<\/h2>\r\n\r\n\r\n\r\n
    \r\n
  1. Persamaan diferensial parsial (metode beda hingga: skema eksplisit, skema implisit, skema Crank Nicholson).<\/li>\r\n
  2. Dasar-dasar metode volume hingga.<\/li>\r\n
  3. Dasar-dasar metode elemen hingga.<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n

    Agenda Kuliah<\/h2>\r\n\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Minggu ke-<\/th>\r\nTopik<\/th>\r\nMateri<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    1<\/td>\r\nPersamaan diferensial parsial (partial differential equations<\/em>, PDE).<\/td>\r\n\r\n
      \r\n
    • Bentuk dan sifat persamaan diferensial parsial (eliptik, parabolik, hiperbolik).<\/li>\r\n
    • Contoh-contoh PDE di bidang teknik sipil (geoteknik, keairan, lingkungan, struktur).<\/li>\r\n
    • Pengantar metode penyelesaian numeris PDE: beda hingga, volume hingga, elemen hingga.<\/li>\r\n
    • PDE eliptik (Persamaan Laplace).<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\nMetode beda hingga (1).<\/td>\r\n\r\n
      \r\n
    • Penyelesaian PDE eliptik (Persamaan Laplace): teknik penyelesaian, syarat batas.<\/li>\r\n
    • Penyelesaian PDE parabolik: metode beda hingga skema eksplisit.<\/li>\r\n
    • PR\/Kuis.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\nMetode beda hingga (2).<\/td>\r\n\r\n
      \r\n
    • PDE parabolik fungsi waktu (time-dependent PDE)<\/em>.<\/li>\r\n
    • Penyelesaian PDE parabolik: metode beda hingga skema implisit sederhana dan skema semi-implisit (metode Crank-Nicolson).<\/li>\r\n
    • PR\/Kuis.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\nMetode volume hingga (1).<\/td>\r\n\r\n
      \r\n
    • Pengantar metode volume hingga: control volume<\/em>, finite volume<\/em>, persamaan diferensial dan integrasi persamaan diferensial.<\/li>\r\n
    • PDE difusi 1D.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\nMetode volume hingga (2).<\/td>\r\n\r\n
      \r\n
    • Penyelesaian PDE difusi 1D.<\/li>\r\n
    • Diskretisasi spasial (pembuatan grid<\/em>\/mesh<\/em>).<\/li>\r\n
    • Diskretisasi persamaan difusi 1D.<\/li>\r\n
    • Contoh hitungan PDE difusi 1D permanen (steady<\/em>), memakai spreadsheet<\/em>.<\/li>\r\n
    • PR\/Kuis.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    6<\/td>\r\nMetode volume hingga (3).<\/td>\r\n\r\n
      \r\n
    • Penyelesaian PDE difusi-konveksi 1D.<\/li>\r\n
    • Diskretisasi spasial dan PDE difusi-konveksi 1D: central difference<\/em>, upwind difference<\/em>).<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    7<\/td>\r\nMetode volume hingga (4).<\/td>\r\n\r\n
      \r\n
    • Diskretisasi PDE difusi-konveksi: hybrid difference<\/em>.<\/li>\r\n
    • Contoh perhitungan PDE difusi-konveksi 1D permanen (steady<\/em>), memakai <\/span>spreadsheet<\/em>.<\/span><\/li>\r\n
    • PR\/Kuis.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    8<\/td>\r\nUTS – Ujian Tengah Semester<\/strong><\/span><\/td>\r\n<\/tr>\r\n
    9<\/td>\r\nPendahuluan metode elemen hingga.<\/td>\r\n\r\n
      \r\n
    • Pengantar metode elemen hingga: mengenal berbagai governing equations<\/em> permasalahan dalam bidang teknik sipil.<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    10<\/td>\r\nMetode elemen hingga (1).<\/td>\r\n\r\n
      \r\n
    • Solusi Boundary Value Problems<\/em>:\r\n
        \r\n
      • The Variational Method, the Rayleigh-Ritz method.<\/em><\/li>\r\n
      • The weighted residual method, trial functions, the Galerkin Method. <\/em><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    11<\/td>\r\nMetode elemen hingga (2).<\/td>\r\n\r\n
      \r\n
    • Potential Energy Formulations.<\/em><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    12<\/td>\r\nMetode elemen hingga (3).<\/td>\r\n\r\n
      \r\n
    • Solusi one-dimensional beam problems.<\/em><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    13<\/td>\r\nMetode elemen hingga (4).<\/td>\r\n\r\n
      \r\n
    • Solusi two-dimensional plane stress problems.<\/em><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    14<\/td>\r\nMetode elemen hingga (5).<\/td>\r\n\r\n
      \r\n
    • Solusi two-dimensional plane strain problems.<\/em><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    15<\/td>\r\nMetode elemen hingga (6).<\/td>\r\n\r\n
      \r\n
    • Solusi two-dimensional plate bending problems.<\/em><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
    16<\/td>\r\nUAS – Ujian Akhir Semester<\/strong><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/figure>\r\n\r\n

    Bahan Kuliah<\/h2>\r\n\r\n\r\n\r\n

    SNPD0 Pengantar<\/a>
    SNPD2 Metode Beda Hingga;\u00a0 \u00a0SNPD2 Metode Beda Hingga b<\/span>
    SNPD2 Metode Beda Hingga c<\/a>
    SNPD3 Metode Volume Hingga;\u00a0 \u00a0SNPD3 Metode Volume Hingga 2025<\/span>
    SNPD3 Metode Volume Hingga 2025b;\u00a0 \u00a0SNPD3 Metode Volume Hingga 2025c<\/span>
    SNPD3 Metode Volume Hingga 2025d<\/a><\/p>\r\n

    Source Code<\/h2>\r\n

    Source Code Difusi 1D | i s t i a r t o<\/a><\/p>\r\n\r\n\r\n\r\n

    Soal Ujian<\/h2>\r\n\r\n\r\n\r\n

    Soal UTS SNPD 2021<\/a>; Penyelesaian Soal UTS SNPD 2021<\/a>
    Soal UTS SNPD 2022<\/a>; Penyelesaian Soal UTS SNPD 2022<\/a>
    Soal UTS SNPD 2023<\/a>; Penyelesaian Soal UTS SNPD 2023<\/a>
    Soal UTS SNPD 2024<\/a>; Penyelesaian Soal UTS SNPD 2024<\/a><\/p>\r\n

    Soal UTS SNPD 2025 TS<\/a>; Soal UTS SNPD 2025 TSDA<\/a>; Penyelesaian Soal UTS SNPD 2025<\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":"

    Mata kuliah “Solusi Numerik Persamaan Diferensial” merupakan salah satu mata kuliah wajib di Program Sarjana DTSL FT UGM, Semester V, 2 sks. Kuliah diselenggarakan dalam 14\u00d7100′ tatap muka, dibagi menjadi dua bagian, masing-masing 7\u00d7100′ tatap muka. Bagian I berlangsung sebelum … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1108,"featured_media":0,"parent":2999,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4885","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/4885","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/users\/1108"}],"replies":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/comments?post=4885"}],"version-history":[{"count":111,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/4885\/revisions"}],"predecessor-version":[{"id":7248,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/4885\/revisions\/7248"}],"up":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/2999"}],"wp:attachment":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/media?parent=4885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}