Solving ODEs with MATLAB

Solving ODEs with MATLAB - Solving ODEs with Matlab :...

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Unformatted text preview: Solving ODEs with Matlab : Instructor’s Manual L.F. Shampine and I. Gladwell Mathematics Department Southern Methodist University Dallas, TX 75275 S. Thompson Department of Mathematics & Statistics Radford University Radford, VA 24142 c 2002, L.F. Shampine, I. Gladwell & S. Thompson 2 Contents 1 Getting Started 5 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Existence, Uniqueness, and Well-Posedness . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Control of the Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Qualitative Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Initial Value Problems 13 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Numerical Methods for IVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 One–Step Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Local Error Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Runge–Kutta Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Explicit Runge–Kutta Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Continuous Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Methods with Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Adams Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 BDF methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Error Estimation and Change of Order . . . . . . . . . . . . . . . . . . . . . . 15 Continuous Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Solving IVPs in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Event Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 ODEs Involving a Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.3 Large Systems and the Method of Lines . . . . . . . . . . . . . . . . . . . . . 22 2.3.4 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Boundary Value Problems 25 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.1 Boundary Conditions at Singular Points . . . . . . . . . . . . . . . . . . . . . 25 3.3.2 Boundary Conditions at Infinity . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Numerical Methods for BVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.5 Solving BVPs in3....
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Solving ODEs with MATLAB - Solving ODEs with Matlab :...

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