Grid method for solution of 2D Riemann type problem with two discontinuities having an initial condition

This study aims to obtain the numerical solution of the Cauchy problem for 2D conservation law equation with one arbitrary discontinuity having an initial profile. For this aim, a special auxiliary problem allowing to construct a sensitive method is developed in order to get a weak solution of the main problem. Proposed auxiliary problem also permits us to find entropy condition which guarantees uniqueness of the solution for the auxiliary problem. To compare the numerical solution with the exact solution theoretical structure of the problem under consideration is examined, and then the interplay of shock and rarefaction waves is investigated.

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ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202508002760 ◽

2008 ◽

Vol 18 (04) ◽

pp. 511-541 ◽

Cited By ~ 22

Author(s):

WENLIANG GAO ◽

CHANGJIANG ZHU

Keyword(s):

Cauchy Problem ◽

Maximum Principle ◽

Coupled System ◽

Model System ◽

Two Dimensions ◽

Rarefaction Waves ◽

Asymptotic Decay ◽

The Maximum Principle ◽

The Cauchy Problem ◽

Asymptotic Decay Rate

In this paper, we consider the asymptotic decay rate towards the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in two dimensions. The analysis based on the standard L2-energy method, L1-estimate and the monotonicity of profile obtained by the maximum principle.

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An Implicit Iterative Method for Numerical Solution of the Cauchy Problem for Elliptic Equations

Journal of Applied and Industrial Mathematics ◽

10.1134/s1990478919040185 ◽

2019 ◽

Vol 13 (4) ◽

pp. 759-770

Author(s):

S. B. Sorokin

Keyword(s):

Cauchy Problem ◽

Iterative Method ◽

Numerical Solution ◽

Elliptic Equations ◽

The Cauchy Problem ◽

Implicit Iterative Method

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2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations

Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations ◽

10.1515/9783110944662.133 ◽

2011 ◽

Keyword(s):

Cauchy Problem ◽

Differential Equations ◽

Numerical Solution ◽

Stochastic Differential Equations ◽

Parabolic Equations ◽

Statistical Simulation ◽

Problem Solution ◽

Elliptic And Parabolic Equations ◽

The Cauchy Problem

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2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.12. Numerical Solution of SDE System with Poisson Component

Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations ◽

10.1515/9783110944662.128 ◽

2011 ◽

Keyword(s):

Cauchy Problem ◽

Differential Equations ◽

Numerical Solution ◽

Stochastic Differential Equations ◽

Statistical Simulation ◽

Problem Solution ◽

The Cauchy Problem ◽

Poisson Component

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ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

Mathematical Modelling and Analysis ◽

10.3846/13926292.2001.9637154 ◽

2001 ◽

Vol 6 (1) ◽

pp. 147-155 ◽

Cited By ~ 1

Author(s):

S. Rutkauskas

Keyword(s):

Boundary Value Problem ◽

Existence And Uniqueness ◽

Boundary Value ◽

Elliptic Systems ◽

Second Order ◽

Type Problem ◽

Dirichlet Type ◽

Holder Class ◽

Uniqueness Of The Solution ◽

Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

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