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The Generalized Difference Method and LDG Method for the Symmetric Regularized Long Wave Equations

Author: YinYanMei
Tutor: XieShuSen
School: Ocean University of China
Course: Computational Mathematics
Keywords: Symmetric regularized long wave equation Generalized Difference Method Local Discontinuous Galerkin Method Convergence Conservation Laws
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 16
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Abstract


Symmetric regularized long wave equation is used to describe the propagation of weakly nonlinear ion-acoustic waves and space charge wave , has many advantages, is an important class of partial differential equations for symmetrical regular long wave equation given solution of the problem posedness and numerical methods the research has attracted more and more attention to the main work of this paper is as follows: the first chapter introduces the symmetric regularized long wave equation physical background and research status , Generalized Difference Method and LDG ( local discontinuous Galerkin ) method of the basic principles of thinking and application . Generalized Difference discrete variational form of the original equation is equivalent to second chapter , symmetric regularized long wave equation generalized difference scheme . using interpolated projection operator and elliptical projection operator , and in the trial function space and testing meet some properties of the function space , fully discrete difference scheme , error estimation, order of convergence estimates obtained format , and proved that the format remains the original equation of conservation laws , and finally , through numerical experiments to verify the convergence and meet the characteristics of the conservation laws . LDG method solving with periodic boundary conditions containing non-linear high order differential symmetric regularized long wave equation initial boundary value problem and proposed the LDG format of the equation , and show that the format of stability and convergence first , the equations into a first order system , select the numerical flux equation to construct LDG format , which proved that the nature of the format to meet the entropy inequality , demonstrate the format of the L2- stable sex , and finally , the use of the nature of the projection operator , inverse estimate inequality , Young 's inequality , gives a detailed error estimate , drawn format convergence order O ( hk ) .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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