Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: porous medium equation

Sortuj według:

Ogranicz wyniki do:

Existence of traveling profiles solutions to porous medium equation

Arioua Yacine, Benhamidouche Nouredine

Journal of Mathematics and Applications

2023

Vol. 46

149--162

In this paper, we shall study the existence and uniqueness of solutions called "traveling profiles solutions" to the porous medium equation in one dimension. By these solutions, we generalize the results obtained by Gilding and Peletier who proved the existence of self similar solutions of type I, II and III to the same equation. The principal idea of our work is to convert the porous media equation in to an equivalent nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.

Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method

Chew J. V. L., Sulaiman J.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 2

11--21

The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.