The Computable Differential Equation Lecture ... - Bruce E. Shapiro

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$NAME: Math 103L: Exercise on Functions ... - Bruce E. Shapiro$

$Introducing Latex - Bruce E. Shapiro$

$Applied Differential Equations, Math 280 at CSUN - Bruce E. Shapiro$

$Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro$

192 CHAPTER 9. DIFFERENTIAL ALGEBRAIC EQUATIONS Example 9.5. The IRK method (3 + √ 3)/6 (3 − √ 3)/6 (3 + √ 3)/6 −( √ 3)/3 0 (3 + √ 3)/6 1/2 1/2 (9.239) has hence it is stable, and 5 = 1 + √ 3 2 + √ 3 hence the overall order of the method is k c = 2. (9.240) k d = 3, k a = 1 (9.241) For a full discussion of Runge-Kutta methods applied to higher index and nonlinear problems the student is referred to [5]. Math 582B, Spring 2007 California State University Northridge c○2007, B.E.Shapiro Last revised: May 23, 2007
Chapter 10 Appendix on Analytic Methods (Math 280 in a Nutshell) This chapter is included for reference only; the level of detail is less than the rest of the notes and only a summary of results is provided. First Order Linear Equations Equations of the form y ′ + p(t)y = q(t) have the solution y(t) = 1 ( ∫ C + µ(t) ) µ(s)q(s)ds where (∫ ) µ(t) = exp p(s)ds t Exact Equations An differential equation M(t, y)dt + N(t, y)dy = 0 is exact if ∂M ∂y = ∂N ∂t in which case the solution is a φ(t) = C where ∫ φ(t, y) = M = ∂φ ∂t , N = ∂φ ∂y ∫ ( ∫ ) ∂M Mdt + N − ∂y dt dy 193
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The Computable Differential Equatio
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Contents 1 Classifying The Problem
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CONTENTS v Timeline on Computable D
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Chapter 1 Classifying The Problem 1
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CHAPTER 1. CLASSIFYING THE PROBLEM
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Chapter 2 Successive Approximations
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CHAPTER 2. SUCCESSIVE APPROXIMATION
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Chapter 3 Approximate Solutions 3.1
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CHAPTER 3. APPROXIMATE SOLUTIONS 45
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Chapter 4 Improving on Euler’s Me
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CHAPTER 4. IMPROVING ON EULER’S M
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Chapter 5 Runge-Kutta Methods 5.1 T
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CHAPTER 5. RUNGE-KUTTA METHODS 91 w
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CHAPTER 5. RUNGE-KUTTA METHODS 93 w
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CHAPTER 5. RUNGE-KUTTA METHODS 95 5
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CHAPTER 5. RUNGE-KUTTA METHODS 97 F
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CHAPTER 5. RUNGE-KUTTA METHODS 99 T
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CHAPTER 5. RUNGE-KUTTA METHODS 101
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Chapter 6 Linear Multistep Methods
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CHAPTER 6. LINEAR MULTISTEP METHODS
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Chapter 7 Delay Differential Equati
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CHAPTER 7. DELAY DIFFERENTIAL EQUAT
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CHAPTER 7. DELAY DIFFERENTIAL EQUAT
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