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Course Co-ordinated by
IIT Kanpur
NPTEL
>> Mathematics >> Numerical Solution of ODEs (Web) >>
Preliminaries
Modules / Lectures
Introduction
Preliminaries
Existence, Uniqueness, and Wellposedness
Stability and Asymptotic Stability
Single Step Methods
The Euler Method
Convergence of Euler’s Method
Improvement of the error bound
Stability
Higher order Single Step Methods
Higher Order Methods
Runge-Kutta Methods
Error bounds for Runge-Kutta methods
Absolute Stability for Runge-Kutta Methods
Systems of Equations and Equations of Order Greater Than One
Systems of Equations
Direct Methods For Higher Order Equations
Consistency, Stability and Convergence of General Single – Step Methods
General Single Step Methods
Convergence of General One-Step Methods
Implicit Runge-Kutta Methods
Derivation of Implicit Runge-Kutta methods
Derivation of Implicit Runge-Kutta Methods(Contd.)
Multistep Methods
Multistep Methods
Multistep Methods(Contd.)
Multistep Methods(Contd..)
The local error of the formulas based on integration
Local Error of Nystrom & Milne-Simpson Methods
Multistep Methods for Special Equations of the Second Order
Special 2nd order equations(Contd.)
Linear Multistep Methods
Linear Multistep Methods
Linear Multistep Methods(Contd)
Consistency and Zero-Stability of Linear Multistep Methods
Convergence of Linear Multistep Methods
Necessary & Sufficient Conditions for Convergence
Absolute Stability and Relative Stability
General methods for finding intervals of absolute and relative stability
Some more methods for Absolute & Relative Stability
Stiff-Initial Value Systems
First order linear systems with constant coefficient
Stiffness and Problem of Stiffness
The problem of implicitness for Stiff systems
Linear multistep methods for Stiff systems
Finite Difference Methods for Boundary Value Problems
Finite Difference Methods
Analysis of Difference System
Analytic Expression of the Error
Nonlinear second order equations
Special Boundary Value Problems
Special Boundary Value Problems(Contd.)
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