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Cahyaningrum, Yuniana
Institut Seni Indonesia Surakarta
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Journal : International Journal of Applied Mathematics and Computing.

 1 
Numerical Analysis and Computational Algorithms in the Simulation of Integral Equations in Applied Mathematics Jimmi Ari Duri; Yuniana Cahyaningrum; Syed Anfal Asif
International Journal of Applied Mathematics and Computing Vol. 1 No. 3 (2024): July : International Journal of Applied Mathematics and Computing
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62951/ijamc.v1i3.266

Abstract

Integral equations are essential tools in applied mathematics, with wide-ranging applications in fields such as physics, engineering, and finance. However, solving these equations presents significant challenges, particularly when dealing with complex, high-dimensional, or singular problems. Traditional methods, such as manual analytical techniques or direct numerical approaches, often struggle with computational efficiency, especially for large-scale systems, and may not be suitable for handling ill-conditioned problems. This study aims to develop an efficient numerical method for solving integral equations by combining adaptive quadrature techniques with Python-based iterative solvers. The adaptive quadrature method adjusts the step size dynamically based on error estimates, ensuring high accuracy even in the presence of singularities or near-singularities, which are common in many real-world problems. The iterative solver, based on Krylov subspace methods, enhances computational efficiency by reducing memory usage and improving the convergence speed of the solution. By using these techniques together, the proposed method significantly improves the computational time required to solve large-scale and complex systems of integral equations, while maintaining satisfactory accuracy. The results demonstrate that the adaptive quadrature technique, when combined with the Python-based iterative solver, offers a substantial advantage in both speed and precision compared to traditional methods. The proposed method is especially effective in handling complex, high-dimensional systems and ill-conditioned problems, making it a powerful tool for applied mathematics, physics, and engineering applications. In conclusion, this study presents a robust and efficient approach for solving integral equations, with potential for future research in solving non-linear and multi-dimensional integral equations.
Co-Authors Abdullah, Maesa Adi Prabowo, Rahayu Adi Saputra, Fajar Afifah Anggara Laksmi Khania Ainun Faridah Alifiyan Al-Ayubi, Achmad Arfiati Nurul Komariah A’imatul Magfiroh Boedy Irhadtanto, Boedy Cahya Surya Harsakya Cerly Sudarta Martsidaun Dani eka ramdhani Day Ramadhani Dian Ratna Puspananda Dwi Sogi Sri Redjeki Eka Ramdhani, Dani Ernia Duwi Saputri Fanlia Prima Jaya Hendrawan, Adam Hidayah, Arinal Istiqomah, Asyifa’ Nur Jasen Eurico Jasen Eurico Jimmi Ari Duri Junarti Junarti Junarti Junarti Kamsariaty Kamsariaty Khuzaini Khuzaini Lusiana, Herlina M. Zainudin Muhammad Ridwan Putra Wijaya Muhammad Rinov Muhammad Rinov Cuhanazriansyah Muhammad Rinov Cuhanazriansyah Nafi'ah, Nurun Neysa , Ai Colleen Nikmah Ayu Ramadhani Amir Novi Mayasari Noviyanti, Nikita Nur Istiqomah, Asyifa’ Nur Istiqomah Prabowo, Rahayu Adi Prasetyo, Ilyas Adhi Pristian, Rika Qolby, Dea Ayu Nurul Ramadhani, Day Ramdhani, Dani Eka Riera, Cin Rinov Cuhanazriansyah, Muhammad Rinov, Muhammad Rizqi Anshori, Faidz Salsabila, Aisyah Fitri Satria Bagus Wibowo Sekar Kinanthi Sely Ayu Lestari Septiani, Dwi Wulan Septianingrum, Salsabila Putri Shulton , Fawaidus Sulastini Sulastini Sutriyanto Syahrial Shaddiq Syahrul Udin Syahrul Udin Syed Anfal Asif undari nurkalis Wangi Quraini, Sekar