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Numerical solution of ordinary differential equations for classical relativistic and nano systems 1st Edition by Donald Greenspan ISBN 3527406107 9783527406104

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Numerical solution of ordinary differential equations for classical relativistic and nano systems 1st Edition Donald Greenspan Digital Instant Download

Author(s): Donald Greenspan
ISBN(s): 9783527406104, 3527406107
Edition: 1
File Details: PDF, 5.15 MB
Year: 2006
Language: english
SKU: EB-1206066 Category: Tag:

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ISBN 10: 3527406107 
ISBN 13: 9783527406104
Author: Donald Greenspan

This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems.

Numerical solution of ordinary differential equations for classical relativistic and nano systems 1st Table of contents:

Chapter 1: Introduction

  • Overview of ODEs in Physical Systems

  • Motivation: Classical, Relativistic & Nano Contexts

Chapter 2: Mathematical Foundations

  • Review of Ordinary Differential Equations

  • Initial Value and Boundary Value Problems

  • Stability and Convergence Basics

Chapter 3: Classical Systems: Numerical Methods

  • Single-Particle Dynamics

  • Multi-Particle Interactions

  • Runge–Kutta Methods & Adaptive Step Size

Chapter 4: Relativistic Dynamics

  • ODEs in Special Relativity

  • Lorentz Force and Charged Particle Motion

  • Numerical Integration under Relativistic Constraints

Chapter 5: Introduction to Nano-Scale ODE Models

  • Nano Physics & ODE Applications

  • Brownian Motion & Langevin Equation

  • Molecular Dynamics Overview

Chapter 6: Advanced Numerical Schemes

  • Multistep Methods and Predictor–Corrector Techniques

  • Symplectic Integrators for Hamiltonian Systems

  • Error Control and Adaptive Approaches

Chapter 7: Practical Implementation Techniques

  • Programming Considerations (C, Python, MATLAB)

  • Efficiency and Performance Optimization

  • Handling Stiff Equations

Chapter 8: Case Studies – Classical Systems

  • Planetary Motion

  • Pendulum and Spring Systems

  • Nonlinear Oscillators

Chapter 9: Case Studies – Relativistic Systems

  • Relativistic Particle in Electromagnetic Fields

  • Synchrotron Motion & Particle Accelerators

Chapter 10: Case Studies – Nano Systems

  • Molecular Dynamics Simulations

  • Nano-Mechanical Resonators

  • Stochastic Simulations

Chapter 11: Convergence, Stability & Error Analysis

  • Global vs. Local Errors

  • Step-Size Sensitivity

  • Long-Term Stability Considerations

Chapter 12: Practical Tips for Complex ODE Systems

  • Choosing the Right Solver

  • Parameter Tuning and Sensitivity Analysis

  • Benchmarking and Validation

Chapter 13: Future Trends & Research Directions

  • Emerging Nano-Scale Modeling

  • Quantum Corrections and Extensions

  • High-Performance Computing Applications

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Tags: Donald Greenspan, Numerical solution, classical relativistic, nano systems