Numerical Solution of ODEs 2GD1DK7PE4

URI	`m2://res/2GD1DK7PE4`
Kind	course
Creators	M.K. Kadalbajoo (instructor)
Scope	in
Ids	course 05pjsgx75:111104030

Expressions

e1: edition

Language	en

m1: page, IIT Kanpur (record). nptel 111104030

Contents

part 1: Introduction
session 1: Preliminaries
session 2: Existence, Uniqueness, and Wellposedness
session 3: Stability and Asymptotic Stability
part 2: Single Step Methods
session 4: The Euler Method
session 5: Convergence of Euler’s Method
session 6: Improvement of the error bound
session 7: Stability
part 3: Higher order Single Step Methods
session 8: Higher Order Methods
session 9: Runge-Kutta Methods
session 10: Error bounds for Runge-Kutta methods
session 11: Absolute Stability for Runge-Kutta Methods
part 4: Systems of Equations and Equations of Order Greater Than One
session 12: Systems of Equations
session 13: Direct Methods For Higher Order Equations
part 5: Consistency, Stability and Convergence of General Single – Step Methods
session 14: General Single Step Methods
session 15: Convergence of General One-Step Methods
part 6: Implicit Runge-Kutta Methods
session 16: Derivation of Implicit Runge-Kutta methods
session 17: Derivation of Implicit Runge-Kutta Methods(Contd.)
part 7: Multistep Methods
session 18: Multistep Methods
session 19: Multistep Methods(Contd.)
session 20: Multistep Methods(Contd..)
session 21: The local error of the formulas based on integration
session 22: Local Error of Nystrom & Milne-Simpson Methods
session 23: Multistep Methods for Special Equations of the Second Order
session 24: Special 2nd order equations(Contd.)
part 8: Linear Multistep Methods
session 25: Linear Multistep Methods
session 26: Linear Multistep Methods(Contd)
session 27: Consistency and Zero-Stability of Linear Multistep Methods
session 28: Convergence of Linear Multistep Methods
session 29: Necessary & Sufficient Conditions for Convergence
session 30: Absolute Stability and Relative Stability
session 31: General methods for finding intervals of absolute and relative stability
session 32: Some more methods for Absolute & Relative Stability
part 9: Stiff-Initial Value Systems
session 33: First order linear systems with constant coefficient
session 34: Stiffness and Problem of Stiffness
session 35: The problem of implicitness for Stiff systems
session 36: Linear multistep methods for Stiff systems
part 10: Finite Difference Methods for Boundary Value Problems
session 37: Finite Difference Methods
session 38: Analysis of Difference System
session 39: Analytic Expression of the Error
session 40: Nonlinear second order equations
session 41: Special Boundary Value Problems
session 42: Special Boundary Value Problems(Contd.)

Catalogue records

nptel: 111104030 (manifestation)