This seminar aims to highlight the important role of modern methods and linear algebra techniques in solving differential equations with its applications arising in science and engineering. The seminar focuses on spectral methods and matrix-based approaches used to analyze and solve complex differential equations. The program brings together researchers and students to share recent developments, research ideas, and practical applications. It provides a platform for knowledge exchange and encourages interdisciplinary collaboration in the fields of mathematics, computational science, and engineering. Participants will gain a deeper understanding of modern algorithms for solving differential equations using numerical methods and linear algebra techniques.