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All Journal BIMASTER Epsilon: Jurnal Matematika Murni dan Terapan Abdimas JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA Edumatsains AKSIOMA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) GERVASI: Jurnal Pengabdian kepada Masyarakat Jurnal Matematika UNAND Technologia: Jurnal Ilmiah Abdimas Galuh: Jurnal Pengabdian Kepada Masyarakat Jurnal Pengabdian kepada Masyarakat Nusantara Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Abdimas Bina Bangsa Komatika: Jurnal Pengabdian Kepada Masyarakat Paulus Civil Engineering Journal Journal of Hospital Administration and Management (JHAM) Jurnal Matematika Integratif Prosiding Seminar Nasional Inovasi Teknologi Terapan Jurnal Inovasi Teknologi Terapan Patisambhida : Jurnal Pemikiran Buddha dan Filsafat Agama Emitor: Jurnal Teknik Elektro
Yudhi
Universitas Tanjungpura
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Journal : AKSIOMA

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Rekonstruksi integrasi numerik metode PIAS segitiga Limanto, Vincent; Yudhi, Yudhi; Prihandono, Bayu
AKSIOMA : Jurnal Matematika dan Pendidikan Matematika Vol 16, No 1 (2025): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/aks.v16i1.19970

Abstract

The solution to numerical integration problems generally can be achieved using mesh methods. However, mesh methods, commonly known as trapezoidal, rectangular, and midpoint, only apply to Cartesian coordinates. Therefore, this research develops a mesh method that can be used for numerical integration in polar coordinates, specifically using Triangle shapes. This study also analyzes the errors from the results of the Triangle mesh method and provides examples and visualizations of applying the Triangle mesh method to solve numerical integration problems. The steps of this research are as follows: first, determining the form of the integral in the problem of numerical integration in polar coordinates. Then, the area bounded by the curve is divided into several parts, each approximated by a triangle. Next, a numerical integration formula of the triangle mesh method is created by summing the areas of each triangle. After that, the resulting error of the triangle mesh method is analyzed using the Taylor series. Finally, proving that the results of the triangle mesh method approximate the area bounded by the curve in polar coordinates. From this research, the numerical integration formula for the Triangle mesh method is obtained, the error formula with a second-order approximation degree, and based on the proof of the numerical integration formula for the Triangle mesh method, it is concluded that as the number of triangles approaches infinity, the results of the Triangle mesh method will converge to the exact area bounded by the curve.
Co-Authors Aan Febriansyah Al Azizi, Fudhail Azzam Thoriqi Aljona, Sarah Amalia Wigati Aminuyati Ammar, Farid Ananda Sapitri, Anjelalica Andi Hairil Alimuddin Andri Royani Anggelina, Florensi Silva Anggraeni, Rosiana Angraini, Wanda Apriliandi Apriliandi Arin Yerliansyah Arya Pratama, Putra Handika Azura, Tina Bayu Prihandono BENI, YAKOBUS Danang Try Purnomo Debataraja, Naomi Nessyana Dedek Noviyani Desi Ayu Wulandari Dessy Natalia Dhea Prameswari Egi Riansyah Eko Sulistyo Evi Novian Evi Noviani FAJRIN NURSETYA DESI Fansiskus Fran Fauzan, M Nur Febriyanto, Ferdy Feby Fitria Ramadhita Feriliani Maria Nani Firman Saputra Fitriani Fitriani Fran, Fransiskus Frananta Maha Fransiskus Fran Fransiskus Fran Hasanuddin Hasanuddin Helmi Helmi Helmi Helmi Helmi Hendra Perdana Huda, Nur’ainul Miftahul Humaira Ichlashi Amaliah Ilham, Muhamad Ilham Irfant Bayu Pratama Irvandi, Firzakalpa Syafiq Iskandar, Rais Khairun Nisa Khariyyah, Lina Laksono Trisnantoro Lili Oktaviana Limanto, Vincent Lita Novianti Lovi Dwi Purnamasari Luluk Hendriyana Mahmul Mahmul Maisurah Maisurah Mareta, Nadia Mariatul Kiftiah Martha, Shantika Maulydiana Septiani Mawarni, Selkia Meiliana Meiliana Meliana Pasaribu Mochammad Imron Awalludin Mudinillah, Adam Muhammad Adiyan Septianda Muhardi Naomi Nessyana Debataraja Neva Satyahadewi Nilamsari Kusumastuti Nopiani Nopiani Novitasari Novitasari Nurfitriana Nurfitriana Nurtaniyahya, Ilham Nurul Fadhilah NUR’AINUL MIFTAHUL HUDA Ocsirendi Okta Rina, Tiara Paranditus Paranditus Paranditus, Paranditus Pramudya, Deby Debora Pratama, Anjeryan Sapta Puteri Islamega Taufani Rabitah Al-Alawiyah ratih ratih Rayhannisa, Rayhannisa Renisa Auditaputri Rian Prasetio Riki Afriansyah Risko, Risko Sahrial Sakti Simanjuntak, Junjungan Dwipa Sandi, Sabinus Saputra, Irpan Selah Siti Nur Amanah Suhardi Tantri, Eliana Tesah Aldi Parani Tri Desrehan, Sagit Tripina, Maria Try Purnomo , Danang Uray Agustian Utari, Dina Wahyu Fahrizal Windarti, Ayu Yanitami, Alvi Yuli Rahayu Yuliardi Kurniawan Yundari, Yundari Yundari, Yundari Yuni Wulandari Yusnanda Yusnanda Zanu Saputra Zettira Septiani