Numerical Solutions of Boundary Value Problems With So-called Shooting Method

Description

"This book presents in comprehensive detail numerical solutions to boundary value problems of a number of differential equations using the so-called Shooting Method. 4th order Runge-Kutta method, Newton's forward difference interpolation method and bisection method for root finding have been employed in this regard. Programs in Mathematica 6.0 were written to obtain the numerical solutions. This monograph on Shooting Method is the only available detailed resource of the topic"-- Contents Preface Chapter 1 Introduction 1.1. Statement of the Problem 1.2. The Methodology of the Numerical Solution Using the So-Called Shooting Method Chapter 2 Differential Equations of Some Elementary Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method 2.1. The Differential Equation for Hyperbolic Function Cosh 2.2. The Differential Equation for Hyperbolic Function Sinh 2.3. The Differential Equation for Cos Function 2.4. The Differential Equation for Sin Function Chapter 3 Differential Equations of Special Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method 3.1. The Hermite Differential Equation and Hermite Polynomial H4 3.2. The Hermite Differential Equation and Hermite Polynomial H5 3.3. The Legendre Differential Equation and Legendre Polynomial P4 3.4. The Legendre Differential Equation and Legendre Polynomial P5 3.5. The Bessel Differential Equation and Bessel Function J0 3.6. The Bessel Differential Equation and Bessel Function J1 Chapter 4 Differential Equation of Airy Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method 4.1. The Airy Differential Equation and Airy Function AiryAi 4.2. The Airy Differential Equation and Airy Function AiryBi Chapter 5 Differential Equation of Stationary Localized Wavepacket: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method 5.1. The Differential Equation of Stationary Localized Wavepacket: Case I 5.2. The Differential Equation of Stationary Localized Wavepacket: Case II Chapter 6 Differential Equation for Motion under Gravitational Interaction: Numerical Solution of Boundary Value Problem with So-Called Shooting Method 6.1. The Differential Equation for Motion under Gravitational Interaction Conclusion Reference About the Authors Index Blank Page