BDP Ch. 8 review sheet

BDP Ch. 8 review sheet - Euler Method (Ex. 1, p. 445)...

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Boyce/9ed/Ch8 Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 9e Chapter 8: Numerical Methods Definitions: 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 Runge-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.
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Unformatted text preview: Euler Method (Ex. 1, p. 445) Backward Euler Method (Ex. 2, p. 447) Improved Euler Method (Ex. 1, p. 455) Runge-Kutta Method (Ex. 1, p. 461) Predictor-Corrector Method, Adams-Bashforth Formula, Adams-Moulton Formula (Ex. 1, p. 467) Backward Differentiation Method (Ex. 2, p. 468) Use numerical methods to find approximate solutions to systems of ODE'S. (Ex. 1, p. 481) Observing large errors of approximation for Eulers method (Ex. 1, p. 471) Use numerical methods to find approximate solutions to stiff ODEs (Ex. 2, p. 475) 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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