Review for midterm examination 1

Review for midterm examination 1 - 16. 10.2.7 17. RK45: 6...

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Review for midterm examination 1 9/29/2011 1. I.V.P. 2. What is a numerical solution to an I.V.P.? 3. Taylor series method of order 1, 2, . ..,m with step length ± ²³´ µ 4. Euler’s method (as a special case) 5. 10.1.8 6. Stability example discussed in class. 10.1.9 7. 10.1.15 8. Carry out Euler’s by hand (for a few steps) 9. Runge-Kutta methods. What the main idea? How to carry out the ideas? 10. Comparison of Taylor with Runge-Kutta: advantage/disadvantage 11. Main tool: Taylor series for two (or more variables) 12. RK2: many possibilities 13. RK4: formulation (the main form) 14. Carry out RK2 by hand (for a few steps) 15. 10.2.4
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Unformatted text preview: 16. 10.2.7 17. RK45: 6 evaluations but with both order 4 and order 5 methods. Estimate the error | | 18. Strategy for an adaptive approach (p. 453) 19. Adams-Bashforth-Moulton formulas: use older values 20. Exact for polynomials of degree 3 (at four points). How to do it? 10.3.4 21. Stability analysis (a baby proof) on page 456-459. 22. 10.3.1-2 23. Write out the Euler for system of two equations. Carry out the computation by hand for a few steps 24. Write out RK4 for system of two equations, ode of order 2 25. Autonomous system/formulation 26. AM method v.s. AM formula...
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