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Computational Physics. Matlab. With. ( Ordinary Differential Equations ). Prof. Muhammad Saeed. Solution of ODEs 1. Initial Value Problems. ODEs of the form:. Euler’s Method. It can be derived from Taylor Series. a) Single-Step Mwthods :. Modified Euler’s Method.
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Computational Physics Matlab With ( Ordinary Differential Equations ) Prof. Muhammad Saeed
Solution of ODEs 1. Initial Value Problems ODEs of the form: • Euler’s Method It can be derived from Taylor Series a) Single-Step Mwthods: M.Sc. Physics
Modified Euler’s Method • Runge-Kutta Methods i) 2nd Order R-K ii) 3rd Order R-K M.Sc. Physics
iii) 4th Order R-K M.Sc. Physics
iii) 5th Order R-K M.Sc. Physics
iii) Runge-Kutta-Fehlberg M.Sc. Physics
b) Multistep Methods: • Adam’s Method • Milne’s Method M.Sc. Physics
Adam-Moulton Method M.Sc. Physics
2. Higher Order Initial Value Problems • Lower Order Conversion Transform the equation into the first order equations. Apply any previous method on the equations simultaneously. • Finite Difference Method Replace all derivatives by difference formulas and form a matrix for function (y) values. 3. System of ODEs M.Sc. Physics
4. Boundary Value Problems • Shooting Method Guess derivative’s initial value and compare the boundary values. • Finite Difference Method 5. Partial Differential Equations • Finite Difference Method Solution of Laplace Equation. M.Sc. Physics
End M.Sc. Physics
