The numerical solution of initial-boundary value problem for nonlinear Fisher’s equation by using non-polynomial spline functions

2015 ◽  
Author(s):  
Serhat Yilmaz
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Polynomial Spline ◽  
Spline Functions ◽  
Fisher’S Equation ◽  
Fisher's Equation ◽  
Initial Boundary Value

scholarly journals On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

2016 ◽  
Vol 10 (4) ◽  
pp. 285-290 ◽  
Author(s):  
Svyatoslav Litynskyy ◽  
Yuriy Muzychuk ◽  
Anatoliy Muzychuk
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Neumann Condition ◽  
Laguerre Transform ◽  
Boundary Elements Method ◽  
Initial Boundary Value

Abstract We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.

scholarly journals Numerical Solution of a Two-Dimensional Problem of Fluid Filtration in a Deformable Porous Medium

2021 ◽  
pp. 88-92
Author(s):  
R.A. Virts
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Deformable Porous Medium ◽  
Balance Of Forces ◽  
Initial Boundary Value

The paper considers a two-dimensional mathematical model of filtration of a viscous incompressible fluid in a deformable porous medium. The model is based on the equations of conservation of mass for liquid and solid phases, Darcy’s law, the rheological relationship for a porous medium, and the law of conservation of the balance of forces. In this article, the equation of the balance of forces is taken in full form, i.e. the viscous and elastic properties of the medium are taken into account. The aim of the work is a numerical study of a model initial-boundary value problem. Section 1 gives a statement of the problem and a brief review of the literature on works related to this topic. In item 2, the original system of equations is transformed. In the case of slow flows, when the convective term can be neglected, a system arises that consists of a second-order parabolic equation for the effective pressure of the medium and the first-order equation for porosity. Section 3 proposes an algorithm for the numerical solution of the resulting initial-boundary value problem. For the numerical implementation, a variable direction scheme for the heat equation with variable coefficients is used, as well as the Runge — Kutta scheme of the fourth order of approximation.

Sign in / Sign up

Export Citation Format

Share Document