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All Journal MATHunesa: Jurnal Ilmiah Matematika Indonesian Journal of Mathematics and Applications
Nurkarimah, Dwi
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Computer Science & IT Education Mathematics Other

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Comparison Study between Shooting and Finite Difference Methods for Solving Linear Boundary Value Problem with Dirichlet, Neumann, and Robin Boundary Conditions Ardiana, Dita; Rachman, Alifira Meliana; Nurkarimah, Dwi; Habibah, Ummu
Indonesian Journal of Mathematics and Applications Vol. 3 No. 1 (2025): Indonesian Journal of Mathematics and Applications (IJMA)
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2025.003.01.2

Abstract

This study conducts a comparative analysis of the Shooting and Finite Difference methods for solving boundary value problems (BVPs) in ordinary differential equations (ODEs). The findings indicate that the Shooting method offers superior accuracy, particularly for smaller step sizes, whereas the Finite Difference method is more straightforward to implement and exhibits greater computational efficiency. The results further demonstrate that the Shooting method is particularly highly appropriate for problems with Dirichlet boundary conditions, as it achieves the lowest mean absolute error (MAE) across various step sizes. Conversely, the Finite Difference method attains higher computational efficiency for the same problem type but performs less advantageously in cases involving other boundary conditions. In contrast, the Shooting method demonstrates greater efficiency in solving problems with Neumann and Robin boundary conditions. The selection of an appropriate numerical method depends on the specific characteristics of the problem, necessitating a balance between accuracy and computational cost. This study provides a comprehensive evaluation of these numerical approaches to support the selection of the most suitable method for efficiently and accurately solving BVPs.
Comparison Study between Shooting and Finite Difference Methods for Solving Linear Boundary Value Problem with Dirichlet, Neumann, and Robin Boundary Conditions Ardiana, Dita; Rachman, Alifira Meliana; Nurkarimah, Dwi; Habibah, Ummu
Indonesian Journal of Mathematics and Applications Vol. 3 No. 1 (2025): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2025.003.01.2

Abstract

This study conducts a comparative analysis of the Shooting and Finite Difference methods for solving boundary value problems (BVPs) in ordinary differential equations (ODEs). The findings indicate that the Shooting method offers superior accuracy, particularly for smaller step sizes, whereas the Finite Difference method is more straightforward to implement and exhibits greater computational efficiency. The results further demonstrate that the Shooting method is particularly highly appropriate for problems with Dirichlet boundary conditions, as it achieves the lowest mean absolute error (MAE) across various step sizes. Conversely, the Finite Difference method attains higher computational efficiency for the same problem type but performs less advantageously in cases involving other boundary conditions. In contrast, the Shooting method demonstrates greater efficiency in solving problems with Neumann and Robin boundary conditions. The selection of an appropriate numerical method depends on the specific characteristics of the problem, necessitating a balance between accuracy and computational cost. This study provides a comprehensive evaluation of these numerical approaches to support the selection of the most suitable method for efficiently and accurately solving BVPs.
PENERAPAN METODE FUZZY TOPSIS INTUISIONISTIK DALAM PEMILIHAN MASKAPAI PENERBANGAN TERFAVORIT DI BANDARA JUANDA SURABAYA Nurkarimah, Dwi; Yunianti, Dwi Nur
MATHunesa: Jurnal Ilmiah Matematika Vol. 11 No. 3 (2023)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v11n3.p391-400

Abstract

Pada era globalisasi perkembangan industri transportasi di Indonesia berkembang dengan pesat. Salah satunya yaitu industri penerbangan. Maskapai penerbangan memiliki peran penting dalam industri ini. Sebagai perusahaan yang mengoperasikan pesawat udara, mereka bertanggung jawab menyediakan layanan transportasi udara yang aman, efisien, dan nyaman bagi penumpang. Keanekaragaman maskapai yang ada terkadang membuat calon penumpang bingung dalam memilih maskapai dengan kualitas terbaik. Dalam penelitian ini, lima maskapai penerbangan akan dipilih yaitu Garuda Indonesia, AirAsia, Lion Air, Batik Air, dan Citilink. Pemilihan maskapai tersebut didasarkan pada hasil survei Top Brand Index tahun 2022 yang menunjukkan preferensi masyarakat terhadap maskapai penerbangan. Responden penelitian ini yaitu pengguna maskapai penerbangan di Bandara Juanda Surabaya yang berusia di atas 18 tahun dan telah menggunakan minimal tiga maskapai penerbangan di bandara tersebut. Pemilihan maskapai terfavorit dinilai berdasarkan enam kriteria dan 13 subkriteria. Kriteria pertama adalah harga dengan subkriteria harga tiket dan diskon. Kriteria kedua adalah pelayanan dengan subkriteria performa pelayanan, pemberian kompensasi, serta kemudahan pembelian dan pemesanan tiket. Kriteria ketiga adalah akurasi jadwal dengan subkriteria penerbangan tanpa transit dan penerbangan tepat waktu. Kriteria keempat adalah fasilitas utama dengan subkriteria kuota bagasi dan klaim bagasi. Kriteria kelima adalah fasilitas pendukung dengan subkriteria pilihan makanan dan minuman, serta hiburan multimedia. Kriteria keenam adalah keamanan dengan subkriteria alat keamanan dan sejarah kecelakaan. Tujuannya adalah menerapkan metode Fuzzy TOPSIS Intuisionistik dalam pemilihan maskapai penerbangan terfavorit di Bandara Juanda Surabaya. Hasil perhitungan menggunakan metode tersebut memberikan rekomendasi maskapai terfavorit dengan nilai koefisien kedekatan relatif sebesar 0,779228993137, yaitu pada Lion Air.Kata Kunci: Pemilihan Maskapai Terfavorit, Metode fuzzy TOPSIS Intuisionistik, Sistem Pendukung Keputusan
Co-Authors Ardiana, Dita Rachman, Alifira Meliana Ummu Habibah, Ummu Yunianti, Dwi Nur