Numerical Solutions Using the Taylor Series Method
Initial and Boundary Value Problems
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Beschreibung
This book discusses the Taylor Series Method for numerical solution of initial and boundary value problems. A number of differential equations related to problems in physics have been solved numerically, including radioactive decay; simple harmonic motion; damped harmonic motion; driven damped harmonic motion; motion of oscillators in phase space, cyclotron motion; and differential equations for Hyperbolic functions. In addition, several Hermite polynomials have been reproduced by numerically solving two-point boundary value problems. Regarding oscillatory motion, the authors present both velocity and displacement of the oscillating particle as functions of time. For cyclotron motion, the authors simulate trajectory of electrons in magnetic field in real space. Also, Hermite polynomials H3, H4 and H5 are reproduced by numerically solving two-point boundary value problems.
In addition, this book:
- Utilizes Mathematica® throughout to perform symbolic computation
- Demonstrates that large increments of the independent variable can be used to obtain agreement with analytic solutions
- Presents solutions of boundary value problems using the shooting method
This book discusses the Taylor Series Method for numerical solution of initial and boundary value problems. A number of differential equations related to problems in physics have been solved numerically, including radioactive decay; simple harmonic motion; damped harmonic motion; driven damped harmonic motion; motion of oscillators in phase space, cyclotron motion; and differential equations for Hyperbolic functions. In addition, several Hermite polynomials have been reproduced by numerically solving two-point boundary value problems. Regarding oscillatory motion, the authors present both velocity and displacement of the oscillating particle as functions of time. For cyclotron motion, the authors simulate trajectory of electrons in magnetic field in real space. Also, Hermite polynomials H3, H4 and H5 are reproduced by numerically solving two-point boundary value problems.
Utilizes Mathematica® throughout to perform symbolic computation Demonstrates that large increments of the independent variable can be used to obtain agreement with analytic solutions Presents solutions of boundary value problems using the shooting method
Autor*in
Sujaul Chowdhury
Themen in »Numerical Solutions Using the Taylor Series Method«
Taylor Series Method Initial Value Problems Two-point Boundary Value Problems Radioactive Decay Simple, Damped, and Driven Damped Harmonic Motion Motion of Oscillators in Phase Space Cyclotron Motion Hyperbolic Function Hermite Polynomials Computational Physics Computational Mathematics