CSC_349_HANDOUT#34

# CSC_349_HANDOUT#34 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 34 ORDINARY DIFFERENTIAL EQUATIONS Part 7 of the textbook: see pages 671-680 (5 th ed.) or pages 697-706 (6 th ed.) for Motivation and Mathematical Background. Recall that the mathematical model of a free- falling body developed in Chapter 1 involved a first order differential equation, and a simple numerical method was developed there for solving that differential equation. Chapter 25 Runge-Kutta methods The problem considered is a first-order initial value problem, which is always assumed to be in the form , ) ) ( , ( ) ( x y x f x y = subject to the initial condition . ) ( 0 0 y x y = Here x is the independent variable, the dependent variable y is a function of x , and f is a given function of both x and ) ( x y that specifies the derivative of the function y . Given constants 0 0 and , y b x a = and a function ) ) ( , ( x y x f , the problem is to determine ) ( x y for b x a . Example Determine 2 0 for ) ( x x y such that 5 . 0 ) 0 ( subject to , 1 ) ( 2 = + = y x y x y .

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CSC_349_HANDOUT#34 - COMPUTER SCIENCE 349A Handout Number...

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