# Numerical Solutions of Initial Value Problems Using Mathematica

- Sujaul Chowdhury, Ponkog Kumar Das

- May 2018

### Description

The book contains a detailed account of numerical solutions of differential equations of a number of elementary problems of physics using Euler and second order Runge–Kutta methods using Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.### About Editors

Sujaul Chowdhury is a Professor in the Department of Physics, Shahjalal University of Science and Technology (SUST), Bangladesh. He obtained a BSc (Honours) in physics in 1994 and an MSc in physics in 1996 from SUST. He obtained a PhD in physics from the University of Glasgow, UK, in 2001. He was a Humboldt Research Fellow for one year at The Max Planck Institute, Stuttgart, Germany.Ponkog Kumar Das is an Assistant Professor in the Department of Physics, SUST. He obtained a BSc (Honours) and MS in physics from SUST. He is a promising future intellect. The work has been done by the two authors using the computational facility in Nanostructure Physics Computational Lab in the Department of Physics, SUST.

### Table of Contents

Chapter I

Numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods

1.1 Euler solution of differential equation

1.2 2nd order Runge-Kutta solution of differential equation

Chapter II

Motion under constant force: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica

2.1 Motion under constant force: the differential equations of themotion

2.2 Euler solution of free fall using Mathematica 6.0

2.3 Runge-Kutta solution of free fall using Mathematica 6.0

Chapter III

Simple harmonic oscillator: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica

3.1 Motion under Hooke's law force: the differential equations of the motion

3.2 Euler solution of simple harmonic oscillation using Mathematica 6.0

3.3 Runge-Kutta solution of simple harmonic oscillation using Mathematica 6.0

Chapter IV

Damped harmonic oscillator: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica

4.1 Damped harmonic oscillator: the differential equations of the motion

4.2 Euler solution of damped harmonic oscillation using Mathematica 6.0

4.3 Runge-Kutta solution of damped harmonic oscillation using Mathematica 6.0

Chapter V

Radioactive decay: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica

5.1 The differential equation for radioactive decay

5.2 Euler solution of radioactive decay law using Mathematica 6.0

5.3 Runge-Kutta solution of radioactive decay law using Mathematica 6.0

Chapter VI

Miscellaneous use of Mathematica in computational Physics

6.1 Dealing with complex numbers using mathematica

6.2 Solution of a system of linear equations using mathematica

6.3 Differentiation and integration using mathematica

6.4 Dealing with matrices using Mathematica

### Bibliographic

Paperback ISBN: 9780750329170

Ebook ISBN: 9781681749754

DOI: 10.1088/978-1-6817-4976-1

Publisher: Morgan & Claypool Publishers