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Initial Value Problems for Ordinary Differential Equations, Slides of Computational Physics

Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS)Computational Physics

This lecture is for Computational Physics course. It was delivered by Dr. Hanif Durad at Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS). It includes: Initial, Value, Problems, Ordinary, Differential, Equations, Numerical, Solution, ODE, Order, Newton, Second, Law

Typology: Slides

2011/2012

Uploaded on 07/19/2012

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Dr. Hanif Durad 2
Lecture Outline
Ordinary differential equation
Numerical Solution of ODEs
Numerical Methods for ODEs
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Download Initial Value Problems for Ordinary Differential Equations and more Slides Computational Physics in PDF only on Docsity!

Dr. Hanif Durad

Lecture Outline

Ordinary differential equation

Numerical Solution of ODEs

Numerical Methods for ODEs

9.1 Differential Equations

Dr. Hanif Durad

Higher-Order ODEs

Dr. Hanif Durad

(1/2)Example: Newton’s Second Law

Dr. Hanif Durad

Ordinary Differential Equations

Dr. Hanif Durad

Initial Value Problems (1/2)

Dr. Hanif Durad

(1/2)Example: Initial Value Problem

Dr. Hanif Durad

(2/2)Example: Initial Value Problem

Dr. Hanif Durad

Example 9.5 ,P-

Example: Stable Solutions

Dr. Hanif Durad

Softwares to be used

Polking at http://math.rice.edu/~dfield/MATLAB by David Arnold & John C.Ordinary Differential Equations using

dfield8 (software for plotting Direction Line field)

pplane8 (software for plotting planar systems)

Dr. Hanif Durad

Using dfield

Dr. Hanif Durad

SolutionsExample: Asymptotically Stable

Dr. Hanif Durad

Example 9.6 ,P-

(1/2)Example: Stability of Solutions

Dr. Hanif Durad

ODEs (1/5)Example: Linear System of

Dr. Hanif Durad