Beginning Scientific Computing

Advanced Differential Equations

Lecture 1

 

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APPLICATION OF RUNGE-KUTTA TO LORENZ EQUATION: We demonstrate the application of the 4th-order accurate Runge-Kutta solver (ODE45) to the classic Lorenz system.

 

MATLAB COMMANDS

ODE45

MATLAB CODE

 

Supplementary Videos

 

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Function Handles in MATLAB
Code: file.m

 

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Vector fields and phase-planes
Code: file.m

Lecture 2

 

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VECTORIZED TIME-STEP INTEGRATORS: We show how ODE time-steppers can be used to study myriad of dynamical trajectories simultaneously in a vectorized form.

 

MATLAB COMMANDS

ODE45

MATLAB CODE

 

Supplementary Videos

 

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Indexing Equations
Code: file.m

 

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Big Systems of ODEs
Code: file.m

Lecture 3

 

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APPLICATION OF RUNGE-KUTTA TO CHAOTIC DYNAMICS AND THE DOUBLE PENDULUM: We finish by considering the physical application of a double pendulum and a numerical model for its motion, demonstrating the chaotic behavior induced in the motion.

 

MATLAB COMMANDS

ODE45

MATLAB CODE

 

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