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Nunung Nurhayati
Universitas Jenderal Soedirman
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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
Solution of the Second Order of the Linear Hyperbolic Equation Using Cubic B-Spline Collocation Numerical Method Kharisa, Aflakha; Maryani, Sri; Nurhayati, Nunung
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 2 (2022): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i2.7496

Abstract

Wave equation is one of the second order of the linear hyperbolic equation. Telegraph equation as a special case of wave equation has interesting point to investigate in the numerical point of view. In this paper, we consider the numerical methods for one dimensional telegraph equation by using cubic B-spline collocation method. Collocation method is one method to solve the partial differential equation model problem. Cubic spline interpolation is an interpolation to a third order polynomial. This polynomial interpolate four point. B-Spline is one of spline function which related to smoothness of the partition. For every spline function with given order can be written as linear combination of those B-spline. As we known that the result of the numerical technique has difference with the exact result which we called as, so that we have an error. The numerical results are compared with the interpolating scaling function method which investigated by Lakestani and Saray in 2010. This numerical methods compared to exact solution by using RMSE (root mean square error), L2 norm error and L_∞ norm error . The error of the solution showed that with the certain function, the cubic collocation of numerical method can be used as an alternative methods to find the solution of the linear hyperbolic of the PDE. The advantages of this study, we can choose the best model of the numerical method for solving the hyperbolic type of PDE. This cubic B-spline collocation method is more efficiently if the error is relatively small and closes to zero. This accuration verified by test of example 1 and example 2 which applied to the model problem.
Co-Authors Agung Prabowo Agung Waluyo Agus Yudianto Agustina, Lisna Agustinus Tandilo Mamma Alfaridzi, Sultan Izbik Riska Alwi, Wahyuni Ambasari, Wulan Novika Anatasya, Anatasya Ani Anggriani, Ani Anjani, Selsa Putri Anna Yuliana, Anna Annisa Nadiyah Rahmani Annysa Ellycornia Silvyana Apriliana, Yhenis Arismunandar, Pandith Aribowo Arvi Iskandar Ashfahani, Raden Ninditya Ghina Astri Mutiar Asyifa Zafira Audina Atmodjo Reubun, Yonathan Tri Ayunazwa Azahra Khaerani Azahra Rizkiah Arifin Arifin Azan, Ferdi Zanuar Bahrul Hayat, Bahrul Baisaku, Nurul Azizah Bhakti Permana Bhakti Permana Budi Aji Budiman Muhamad Cahyono, Habib Citra Nurintan Amelia Dede R Oktini Dewi Sartika Dewi Srinatania Dian Wulandari Dina Aziza Putri Dinda Norma Adelin Dudung Muhally Hakim Dwi Sarwani Sri Rejeki Dyah Mitri Kusuma Wardani Eka Setiawati Elly Halimatusadiah Elly Sukmanasa Elva Kartikasari Elva Kartikasari Esvandiari, Megia Eva Supriatin Eva Supriatin, Eva Farida Isroani Fitria Damayanti, Fitria Friyanti, Ita Halim, Nurfadhlina Abdul Hantoro Ksaid Notolegowo Hardy Hutahaean Hening Pujasari I Made Kariasa Idha Sihwaningrum Ima Amaliah Indy Nur Sholikhah Intan, Dewi Iskandar, Choirunnisa Izzaturahman, Muhammad Khalid Jaenudin, Dadang jajang Jajang Jajang Jajang Jajang Jajang Jambari, Obay Julianti, Eri Kania Nurcholisah Kharisa, Aflakha Khayla, Rahmalia Putri Kristy Kristy Kristy, Kristy Kusumasari, Wardany Ladewi, Yuhanis Lindayani, Linlin Linlin Lindayani Linlin Lindayani Lis Djuniar M Rakan M Riszky Apriliansyah saputra Marcellia Susan Maryani, Sri Mohammad Nauval Alim Mohammad Wildan Alghifari Zain Mufida, Suci Jena Muhammad Agis Ruslan Zaelani Muhammad Fajar Muhardi Muhardi Muhardi Mulyaningsih, Hendrati Dwi Nadiyah Rahmani, Annisa Nana Supriatna Sonjaya Nandang Ihwanudin Nugroho, Arief Styo Nurfahmiyati Nurleli Nyayu Nina Putri Calisanie Oki Neswan Pertiwi, Ratna Prasetya, Gandara Catur Pratiwi, Elsa Anna Puji Siswanto Pupung Purnamasari Putra, Muhamad Zidane Dwita Putri Pradani Putri Pradani Rahayu , Feronika Evma Rahayu, Annisa Eka Rahayuningsih, Nurjanah Rahma, Icha Saeful Raisha Ramadhania Azzahra Ramdhani Rayhan Azis Renando, Nindy Antikasari Renny Ridwan Rina Reorita Rini Lestari Ririn Sk Risna Yuntami Seftianti Riyang Mardini Rizqi, Safina Sabila ROHIMAH, INTAN Rotua Suriany Simamora Runi Hasnidarini Ruthi Armita Sari Ruthi Armita Sari, Ruthi Armita Sali Rahadi Asih Salum Cantika Putri Samsul Anwar Samsul Anwar Sani, Aluwi Nirwana Selia Oktavianti Septa Permana Setiadi, Feri Setiawan, Asep Rudini Sholihah, Hani Siddik, Galih Purnama Siti Maryam, Shabrina Siti Rahmah Nurshiami, Siti Rahmah SR, Dwi Sarwani SR, Dwi Sarwani Sri Fadilah Sri Maryani Suci Noor Hayati Supriyanto Supriyanto Supriyanto Supriyanto Suripah Suripah Susy Puspasari Tasya Aspiranti Tiara Wulandari Tri Wintolo Apoko Tripena Br.Sb, Agustini Tsurayya, Lulu Udin Saripudin Udjianna Sekteria Pasaribu Vannisa Regita Putri Wahyuni Alwi Wardiana, Taufiq Akbar Warti, Lia Wati, Puri Kresna Y Yusdiana Yanti, Dharma Yeni Rumyani Yhenis Apriliana Yuni Fitria Agung Yuyum Yuningsih Zahra, Aliyah