Course Details
Subject {L-T-P / C} : MA6633 : Numerical Solutions of ODE and PDE { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Jugal Mohapatra
Syllabus
• Numerical Solution of Ordinary Differential Equations – Initial-value problems Boundary-value problems: the shooting method, finite difference methods Galerkin method.
• Numerical Solution of Partial Differential Equations – Initial/boundary value problems for parabolic and hyperbolic PDEs (one space and one time dimension) Explicit finite-difference schemes. Implicit finite-difference schemes. Stability Parabolic and hyperbolic PDEs in two space dimensions Boundary value problems for elliptic PDEs.
Course Objectives
- This is an advanced postgraduate-level course in numerical techniques for ordinary and partial differential equations (ODE, PDE). It is required of all graduate students in Applied Mathematics and Mathematical Physics. Using several examples, this course examines conventional numerical techniques for ODE and PDE problems, as well as the characteristics of these approaches. The course will offer applied mathematicians and applied scientists with the foundational knowledge and expertise needed to work with numerical techniques.
Course Outcomes
Numerical approaches for solving initial-value and boundary-value problems for ordinary differential equations. Numerical solutions to initial/boundary value problems for parabolic and hyperbolic linear partial differential equations. Boundary value difficulties for elliptic linear partial differential equations PDEs. Stability of numerical solutions, estimates of errors, and convergence.
Essential Reading
- Richard L. Burden and J. Douglas Faires, "Numerical Analysis", BROOKS/COLE , 2011
- S. Saha Ray, “Numerical Analysis with Algorithms and Programming”, CRC Press , Taylor and Francis Group, 2016
Supplementary Reading
- Kendall E. Atkinson, Weimin Han, David Stewart, "Numerical Solution of Ordinary Differential Equations", Wiley , 2009
- E. Süli, D. F. Mayers, "An Introduction to Numerical Analysis", Cambridge University Press , 2003