ch08 - • Improved Euler Method(Example 1 p.453 •...

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Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 8e Chapter 8: Numerical Methods Definitions and Algorithms: Convergence Global truncation error Local truncation error Round-off error Euler method, backward Euler method Improved Euler method (Heun formula) Modified Euler formula Runga-Kutta method Adaptive methods One-step method Multi-step method, Predictor-corrector method, Adams- Bashforth formula, Adams-Moulton formula, Backward differentiation formulas Stability Stiff Problems Theorems: None Important Skills: Use a particular method with specified step size to compute approximate solutions to ODE's. Euler Method (Example 1, p.443); Backward Euler Method (Example 2, p.445)
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Unformatted text preview: • Improved Euler Method (Example 1, p.453) • Runga-Kutta Method (Example 1, p.459) • Predictor-corrector method, Adams-Bashforth formula, Adams-Moulton formula (Example p.465) • Backward Differentiation Method (Example 2, p.466) • Use numerical methods to find approximate solutions to systems of ODE'S. (Example 1, p.479) • Observing large errors of approximation for Euler’s method (Example 1, p. 469) • Use numerical methods to find approximate solutions to stiff ODE’s (Example 2, p. 473) Relevant Applications: • Any of the applications previously mentioned, where analytical solutions cannot be found, or for which finding analytical solutions are too costly....
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This note was uploaded on 02/22/2010 for the course MATH 23 taught by Professor Dorothywallace during the Spring '10 term at Dartmouth.

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