求解非线性薛定谔方程和KdV-Burger's方程的Pade Sumudu Adomian分解方法
发布时间：2023-05-22 03:34
本文的以一些分析和数值方法为基础,利用Sumudu变换,Adomian分解方法(ADM),和Pade近似技术等方法,求解一些重要的线性和非线性偏微分方程(PDEs)。Sumudu变换法只能求解线性PDE;Sumudu Adomian分解方法(SADM)是Sumudu变换和Adomian分解方法的结合,此方法适用于求解非线性PDE,但是该方法收敛半径小,而且对于某些PDE,利用SADM方法所得的截断级数在很多区域都是不准确的.针对这种情况,本文将通过使用双Pade近似的函数来执行SADM解决方案.我们得到的PSADM解的收敛域大于SADM解.本文使用Adomian多项式计算非线性项,并使用Pade近似来控制级数解的收敛性。我们从方法的基本定义,定理和性质开始,介绍了所提数值方法的研究背景.以上方法可以用于研究一些科学和工程问题的数值解,如线性和非线性薛定谔方程,线性克莱恩-戈登方程,非线性伯格斯方程等.接下来我们提出了该方法基本思想的基本数学公式,数值实验表明了该方法的有效性和高精度.此外,我们给出了该方法求解三维曲面的图形化的数值模拟。所提出的方法为我们提供了一种利用不同阶的帕德近似来...
【文章页数】：102 页
【学位级别】：硕士
【文章目录】：
ABSTRACT
摘要
Chapter 1 Introduction
Chapter 2 Background Materials
2.1 Sumudu transform
2.1.1 Basic definitions and properties of the Sumudu transform
2.1.2 The Laplace-Sumudu duality and the complex Sumudu in-version formula
2.2 Adomian Decomposition Method
2.2.1 Adomian Decomposition Method for Solving nonlinear prob-lems
2.3 Application of the Sumudu decomposition method (SDM) for Lin-ear partrial differential equations
2.4 Pade approximation
2.4.1 Test experiments of Pade approximation
2.5 SADM and PSADM for solving nonlinear PDEs
2.5.1 Procedure for solving (2.54) by SADM
2.5.2 Procedure for solving (2.54) by PSADM
2.5.3 Theory on the nonlinear Schrodinger Equations
2.5.4 Theory on the KdV Burger's equation
Chapter 3 SADM and PSADM for solving Schrodinger and KdVBurger's equations
3.1 SADM and PSADM for solving General Nonlinear Schrodingerequation
3.1.1 Application 1
3.1.2 Application 2: One Dimensional Nonlinear Schrodinger E-quation with Harmonic Oscillator
3.2 SADM and PSADM for solving compound KdV-Burger's equations
3.2.1 Application: p＝-6, q=0, r=0,β=-1,u(x,0)=-2sech2(x)
3.2.2 Application: p≠0,q=0,r≠0,β≠0, KdV-Burgersequation
3.2.3 Application: p≠0,q=0,β=0, Burger's equation
3.2.4 Application: q≠0,p＝0,β≠0, r=0, mKDV Burger'sequation
3.2.5 Application:p=0,q≠0,r≠0,β≠0,mKdV-Burger'sequation
3.2.6 Application: General KdV-Burger's equation
Chapter 4 Conclusions and Prospects
4.1 Conclusions
4.2 Prospects
References
Acknowledgment
学位论文评阅及答辩情况表
本文编号：3821920
【文章页数】：102 页
【学位级别】：硕士
【文章目录】：
ABSTRACT
摘要
Chapter 1 Introduction
Chapter 2 Background Materials
2.1 Sumudu transform
2.1.1 Basic definitions and properties of the Sumudu transform
2.1.2 The Laplace-Sumudu duality and the complex Sumudu in-version formula
2.2 Adomian Decomposition Method
2.2.1 Adomian Decomposition Method for Solving nonlinear prob-lems
2.3 Application of the Sumudu decomposition method (SDM) for Lin-ear partrial differential equations
2.4 Pade approximation
2.4.1 Test experiments of Pade approximation
2.5 SADM and PSADM for solving nonlinear PDEs
2.5.1 Procedure for solving (2.54) by SADM
2.5.2 Procedure for solving (2.54) by PSADM
2.5.3 Theory on the nonlinear Schrodinger Equations
2.5.4 Theory on the KdV Burger's equation
Chapter 3 SADM and PSADM for solving Schrodinger and KdVBurger's equations
3.1 SADM and PSADM for solving General Nonlinear Schrodingerequation
3.1.1 Application 1
3.1.2 Application 2: One Dimensional Nonlinear Schrodinger E-quation with Harmonic Oscillator
3.2 SADM and PSADM for solving compound KdV-Burger's equations
3.2.1 Application: p＝-6, q=0, r=0,β=-1,u(x,0)=-2sech2(x)
3.2.2 Application: p≠0,q=0,r≠0,β≠0, KdV-Burgersequation
3.2.3 Application: p≠0,q=0,β=0, Burger's equation
3.2.4 Application: q≠0,p＝0,β≠0, r=0, mKDV Burger'sequation
3.2.5 Application:p=0,q≠0,r≠0,β≠0,mKdV-Burger'sequation
3.2.6 Application: General KdV-Burger's equation
Chapter 4 Conclusions and Prospects
4.1 Conclusions
4.2 Prospects
References
Acknowledgment
学位论文评阅及答辩情况表
本文编号：3821920
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