From: ₹500.00
Computing forms a key component of Numerical Analysis of ODEs. This workshop aims to develop an understanding of how to translate numerical ideas into efficient code. The programming language used will be Python, though the concepts and techniques are easily transferable to other languages.
Dr. Abhinav Jha is an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Gandhinagar. His research interests lie in Numerical Analysis and Scientific Computing. In addition to the theoretical analysis of numerical methods, he has a strong interest in their efficient and robust implementation on modern computing architectures. His work includes two large-scale computational projects—one developed in C++ and the other in FORTRAN—focusing on the numerical solution of partial differential equations.
| Day | Module name | Concepts covered | Live sessions - No. of hours | Assessment | Learning outcomes |
| 09/05/26 | Introduction to Differential Equations & Euler Method | Modelling using differential equations, IVP vs BVP, geometric interpretation of derivative, slope approximation, discretization, derivation of Euler method | 3 Hours | Manual computation of one Euler step and implementation of Euler method in Python | Understand how derivatives represent slope and how differential equations can be solved numerically through iteration |
| 09/05/26 | Modified Euler Method & Error Analysis | Limitations of Euler method, predictor–corrector idea, Modified Euler/Heun method, step size influence, local and global error | 2 Hours | Modify Euler code to implement Heun method and compare numerical errors graphically | Ability to improve numerical accuracy and interpret the effect of step size and method order |
| 10/05/26 | Runge–Kutta Methods (RK2 & RK4) | Midpoint method (RK2), RK4 algorithm, order of accuracy, comparison of Euler, Heun and RK4 | 3 Hours | Implement RK2 and RK4 in Colab and generate comparison table of errors | Select appropriate numerical solver and evaluate accuracy vs computational effort |
| 10/05/26 | Finite Difference Method for Boundary Value Problems | Second-order ODEs, finite difference approximations, formation of tridiagonal linear systems, matrix formulation, solving using NumPy | 2 Hours | Construct coefficient matrix and solve a boundary value problem |
Convert differential equations into linear algebra systems and compute numerical solutions using Python |
Students – Rs. 590 (Rs. 500 + 18% GST)
Faculty/PostDocs – Rs. 1416 (Rs. 1200 + 18% GST)
Industry – Rs. 1770 (Rs. 1500 + 18% GST)
Intended Audience:
UG, PG, PhD Students, PostDocs/Faculty and Industry.
Eligibility:
Basics of Pythons are expected. If the students want, the Basics can also be covered in the Preliminary classes.
Pre - requisite:
Python will be used. It is a free version.
Attendance is mandatory for obtaining the certificate.
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