• Home
  • Textbooks
  • Principles of Mathematical Modelling: Ideas, Methods, Examples
  • DERIVATION OF MODELS FROM THE FUNDAMENTAL LAWS OF NATURE

Principles of Mathematical Modelling: Ideas, Methods, Examples

Alexander A. Samarskii (Author); Alexander P. Mikhailov

Chapter 2

DERIVATION OF MODELS FROM THE FUNDAMENTAL LAWS OF NATURE - all with Video Answers

Educators


Section 1

Conservation of the Mass of Substance

Problem 1

Find out the transformation of variables reducing equation (1) to equation (3), and show that the solution when $u=u(t)$ has the form (4), where $\xi=x+$ $\int_0^t u(t) d t$.

Check back soon!

Problem 2

The solution of equation (13) of the form $h(x, t)=u(t) \theta(x)$ (i.e. in separating variables) is called regular regime of Bussinesque in the case $u(t) \rightarrow 0, t \rightarrow \infty$. Show that $u(t)$ is a power function of time at large $t$.

Check back soon!

Problem 3

Establish at what assumptions the equation (12) is reduced to the equation of Laplace.

Check back soon!
02:20

Problem 4

Using the law of conservation of mass and the Darsi law, derive equation (15).

Adriano Chikande
Adriano Chikande
Numerade Educator