scholarly journals Explicit Runge–Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems

2010 ◽  
Vol 48 (6) ◽  
pp. 2019-2042 ◽  
Author(s):  
Erik Burman ◽  
Alexandre Ern ◽  
Miguel A. Fernández
Keyword(s):  
Finite Elements ◽  
Order Linear ◽  
First Order ◽  
Linear Pde ◽  
Pde Systems ◽  
Runge Kutta

scholarly journals Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Sankar Prasad Mondal ◽  
Susmita Roy ◽  
Biswajit Das
Keyword(s):  
Differential Equation ◽  
Error Analysis ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Fuzzy Environment ◽  
Runge Kutta ◽  
Linear Differential

The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application.

scholarly journals Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry

2017 ◽  
Author(s):  
Sankar Prasad Mondal ◽  
Susmita Roy ◽  
Biswajit Das ◽  
Animesh Mahata
Keyword(s):  
Numerical Solution ◽  
Kutta Method ◽  
Order Linear ◽  
First Order ◽  
Generalized Hukuhara Derivative ◽  
Fuzzy Environment ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Linear Differential ◽  
Fuzzy Solutions

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

scholarly journals Two scale defect measure and linear equations with oscillating coefficients

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2867-2873
Author(s):  
Jelena Aleksic ◽  
Stevan Pilipovic
Keyword(s):  
Linear Equations ◽  
Convergent Sequence ◽  
Dimensional Torus ◽  
Strong Limit ◽  
Absolutely Continuous ◽  
Order Linear ◽  
First Order ◽  
Linear Pde ◽  
Defect Measure ◽  
Oscillating Coefficients

Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u ? L2(Rd x Td), Td is a torus, to analyze possible strong limit. ? is an operator valued measure absolutely continuous with respect to the product of scalar microlocal defect measure and a measure on the d-dimensional torus. The result is applied to the first order linear PDE with the oscillating coefficients.

Nappes d'huile: prediction de leurs deplacements comme agent efficace d'un plan de mesure d'urgence

1979 ◽  
Vol 14 (1) ◽  
pp. 89-109
Author(s):  
B. Coupal ◽  
M. de Broissia
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Finite Elements ◽  
Mass Balance ◽  
Stochastic Method ◽  
Stochastic Methods ◽  
Deterministic Approach ◽  
First Order ◽  
The Third ◽  
Comme Agent

Abstract The movement of oil slicks on open waters has been predicted, using both deterministic and stochastic methods. The first method, named slick rose, consists in locating an area specifying the position of the slick during the first hours after the spill. The second method combines a deterministic approach for the simulation of current parameters to a stochastic method simulating the wind parameters. A Markov chain of the first order followed by a Monte Carlo approach enables the simulation of both phenomena. The third method presented in this paper describes a mass balance on the spilt oil, solved by the method of finite elements. The three methods are complementary to each other and constitute an important point for a contingency plan.

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