Differential Equations
Lecture 1
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ORDINARY DIFFERENTIAL EQUATIONS AND TIME-STEPPING: Using the definition of derivative and Taylor series, numerical time-stepping schemes are produced for predicting the future state of ODE systems.
MATLAB COMMANDS
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MATLAB CODE
Lecture 2
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ERROR AND STABILITY OF TIME-STEPPING SCHEMES: The accuracy and stability of time-stepping schemes are considered and compared on various time-stepping algorithms.
MATLAB COMMANDS
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Lecture 3
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GENERAL TIME-STEPPING AND RUNGE-KUTTA SCHEMES: A general framework for time-stepping schemes is developed, culminating in the 4th-order accurate Runge-Kutta scheme which is the work-horse of many applications.
MATLAB COMMANDS
ODE45
Supplementary Videos
