1550078481-Ordinary_Differential_Equations__Roberts_

The Initial Value Problem y' = f(x, y); y(c) = d 103 A simple single-step, predictor-corrector method, for instance, might em- p ...

104 Ordinary Differential Equations per step; (3) the maximum number of iterations, K , to be taken per step; and ( 4) what to d ...

The Initial Value Problem y' = f(x, y); y(c) = d 105 Convergence and Instability A numerical method for approximating a solution ...

106 Ordinary Differential Equations SOLUTION We easily find the exact solution of the given linear initial value problem to be y ...

The Initial Value Problem y' = f(x, y); y(c) = d 107 disadvantages of requiring starting values, occasionally being numerically ...

108 Ordinary Differential Equations The numerical results and graphical output presented in examples 8, 9, 10, and 11 were gener ...

The Initial Value Problem y' = f(x, y); y(c) = d 109 y(x) -1 0 1 2 3 4 x Figure 2.14 Direction Field and Graph of a Numerical Ap ...

110 Ordinary Differential Equations SOLUTION Mathematical Analysis The differential equation of (27) is linear with a(x) = 1/((x ...

The Initial Value Problem y' = f(x, y) ; y(c) = d 111 15 10 y(x) 5 0 -2.5 -2 -1. 5 - 1 -0. (^5 0) 0.5 x Figure 2.15 Numerical Ap ...

112 Ordinary Differential Equations rectangle which does not contain a point of the x-axis, where y = 0. So by the fundamental t ...

The Initial Value Problem y' = f(x, y); y(c) = d -2 -1 0 1 2 x Figure 2.16 Graph of a Numerical Approximation of the Solution to ...

114 Ordinary Differential Equations we see that a solution exists as long as (x, y(x)) remains in the first or third quadrant or ...

The Initial Value Problem y' = f(x, y); y(c) = d 115 b. In this case, SOLVEIVP generated a numerical approximation on the interv ...

116 Ordinary Differential Equations y' = y^2 on [-5, 5] a. y(-1) = 1 b. y(-1)=0 c. y(l) = .5 6. y' = y^3 on [-2, 2] a. y(-1) = ...

Chapter 3 Applications of the Initial Value Problem y' = f(x, y) ; y(c) = d In this chapter, we consider a variety of applicatio ...

118 Ordinary Differential Equations FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS If f ( x) is continuous on the interval [a , b] and ...

Applications of the Initial Value Problem y' = f(x, y); y(c) = d 119 Hence, the integral y(x) = 1x J(t) dt is equivalent to y(x) ...

120 Ordinary Differential Equations In what follows we summarize some results and formulas from calculus for computing area, arc ...

Applications of the Initial Value Problem y' = f(x, y); y(c) = d 121 Volumes of Solids of Revolution Let J(x) and g(x) be contin ...

122 Ordinary Differential Equations Formulas Involving Curves Defined Parametrically Area If y( x) is a nonnegative, continuous ...