scholarly journals A novel second order accurate hybrid numerical approach for conservation laws

2008 ◽  
Vol 25 ◽  
pp. 91-113
Author(s):  
Pascal Jaisson ◽  
Florian De Vuyst
Keyword(s):  
Conservation Laws ◽  
Numerical Approach ◽  
Second Order

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

scholarly journals Second-Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yongtao Xuan ◽  
Rohul Amin ◽  
Fakhar Zaman ◽  
Zohaib Khan ◽  
Imad Ullah ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Approach ◽  
Haar Wavelet ◽  
Second Order ◽  
Algebraic Equations ◽  
Elimination Algorithm ◽  
Collocation Points ◽  
Delay Differential ◽  
Mean Square Errors

In this article, an efficient numerical approach for the solution of second-order delay differential equations to deal with the experimentation of the Internet of Industrial Things (IIoT) is presented. With the help of the Haar wavelet technique, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for various collocation points. The results show that the Haar wavelet method is an effective method for solving delay differential equations of second order. The convergence rate is also measured for various collocation points, which is almost equal to 2.

scholarly journals Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 487 ◽  
Author(s):  
Mario Versaci ◽  
Giovanni Angiulli ◽  
Alessandra Jannelli
Keyword(s):  
Convergence Analysis ◽  
Electrostatic Field ◽  
Mean Curvature ◽  
Mechanical Systems ◽  
Numerical Approach ◽  
Second Order ◽  
Circular Membrane ◽  
Differential Model ◽  
The Mean

In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.

scholarly journals On a Theory for Analysing Second-Order Systems of Ordinary Discrete Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
J. J. H. Bashingwa ◽  
A. H. Kara
Keyword(s):  
Conservation Laws ◽  
Difference Equations ◽  
Second Order ◽  
Discrete Equations ◽  
Second Order Systems

We present geometric based methods for solving systems of discrete or difference equations and introduce a technique for finding conservation laws for such systems.

Conformal conservation laws for second-order scalar fields

1976 ◽  
Vol 34 (2) ◽  
pp. 319-324 ◽  
Author(s):  
J. S. Blakeslee ◽  
J. D. Logan
Keyword(s):  
Conservation Laws ◽  
Scalar Fields ◽  
Second Order

WENO-TVD schemes for hyperbolic conservation laws

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Yousef Hashem Zahran
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Building Blocks ◽  
Second Order ◽  
Third Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Systematic Assessment ◽  
The Third ◽  
Seventh Order

The purpose of this paper is twofold. Firstly we carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [14] and [15].This modification is done by using two fluxes as building blocks in spatially fifth order WENO schemes instead of the second order TVD flux proposed by Titarev and Toro [14] and [15]. These fluxes are the second order TVD flux [19] and the third order TVD flux [20].Secondly, we propose to use these fluxes as a building block in spatially seventh order WENO schemes. The numerical solution is advanced in time by the third order TVD Runge–Kutta method. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws, in one and two dimension is presented. Systematic assessment of the proposed schemes shows substantial gains in accuracy and better resolution of discontinuities, particularly for problems involving long time evolution containing both smooth and non-smooth features.

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