ch08 - Improved Euler Method (Example 1, p.453) Runga-Kutta...

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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 Eulers method (Example 1, p. 469) Use numerical methods to find approximate solutions to stiff ODEs (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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