發(fā)布時(shí)間：2019-03-02 17:54

【摘要】：非齊次電報(bào)方程作為一類特殊的非線性發(fā)展型偏微分方程,在電學(xué)、光學(xué)、聲學(xué)以及微波技術(shù)等領(lǐng)域中得到了廣泛應(yīng)用.除極少數(shù)情況外,該方程的解析解是難以求得的,只能通過(guò)數(shù)值方法求其近似解,因此對(duì)于非齊次電報(bào)方程的數(shù)值方法研究具有極其重要的理論意義和應(yīng)用價(jià)值.本文的創(chuàng)新之處是本文主要研究非齊次電報(bào)方程定解問(wèn)題的無(wú)網(wǎng)格特解方法.首先,通過(guò)有限差分方法離散方程中的時(shí)間導(dǎo)數(shù)；其次,適當(dāng)選取徑向基函數(shù)對(duì)未知函數(shù)及其空間導(dǎo)數(shù)進(jìn)行逼近；最后通過(guò)逐層求解配置矩陣得到方程的數(shù)值解.本文結(jié)構(gòu)安排如下：緒論中主要介紹本文的研究背景、研究方法、所考慮問(wèn)題的研究現(xiàn)狀及本文的主要研究工作；第二章,在給出徑向基函數(shù)的相關(guān)概念后詳細(xì)論述徑向基函數(shù)的插值理論；第三章,介紹無(wú)網(wǎng)格方法中,基于徑向基函數(shù)的三種基本數(shù)值方法；第四章,利用無(wú)網(wǎng)格特解方法數(shù)值求解非齊次電報(bào)方程并通過(guò)數(shù)值算例說(shuō)明該方法對(duì)其方程的有效率和穩(wěn)定性.第五章,本文工作總結(jié)及后續(xù)研究展望.
[Abstract]:As a kind of special nonlinear evolution partial differential equation, the inhomogeneous telegram equation has been widely used in the fields of electricity, optics, acoustics and microwave technology. With the exception of a few cases, the analytical solution of the equation is difficult to obtain, and the approximate solution can only be obtained by numerical method. Therefore, it is of great theoretical significance and practical value to study the numerical method of inhomogeneous Telegraph equation. The innovation of this paper is that the meshless special solution method for inhomogeneous telegram equation is studied in this paper. Firstly, the time derivative of the equation is discretized by the finite difference method; secondly, the radial basis function is selected to approximate the unknown function and its spatial derivative; finally, the numerical solution of the equation is obtained by solving the configuration matrix layer by layer. The structure of this paper is arranged as follows: the introduction mainly introduces the research background, research methods, the status quo of the problems considered and the main research work of this paper; In chapter 2, the interpolation theory of radial basis function is discussed in detail after the concept of radial basis function is given, and in chapter 3, three basic numerical methods based on radial basis function are introduced in meshless method. In chapter 4, the meshless special solution method is used to solve the inhomogeneous telegram equation, and the numerical examples are given to illustrate the efficiency and stability of the method to the equation. The fifth chapter summarizes the work of this paper and looks forward to the follow-up research.
【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 廖勇;徐剛;謝平;石小燕;陸巍;丁恩燕;楊周炳;孟凡寶;;非線性傳輸線數(shù)值模擬方法[J];強(qiáng)激光與粒子束;2015年08期

2 謝平;徐剛;廖勇;石小燕;楊周炳;;非線性傳輸線產(chǎn)生射頻脈沖原理研究[J];強(qiáng)激光與粒子束;2014年04期

3 郭鵬;陳宗廣;孫小偉;;非線性電報(bào)方程的簡(jiǎn)潔解法[J];大學(xué)物理;2014年04期

4 褚洪學(xué);姜同松;;求解一類線性反應(yīng)擴(kuò)散方程的特解方法[J];聊城大學(xué)學(xué)報(bào)(自然科學(xué)版);2013年02期

5 王曉蕾;姜同松;;兩種求解一類二維熱傳導(dǎo)方程的無(wú)網(wǎng)格數(shù)值算法的比較[J];臨沂大學(xué)學(xué)報(bào);2012年06期

6 張能偉;郭欣;;帶有非線性阻尼項(xiàng)的非線性電報(bào)方程的cauchy問(wèn)題[J];安陽(yáng)師范學(xué)院學(xué)報(bào);2012年05期

7 戚祖敏;張軍;鐘輝煌;張點(diǎn);;利用非線性傳輸線產(chǎn)生高功率射頻場(chǎng)[J];強(qiáng)激光與粒子束;2012年04期

8 楊中兵,徐萬(wàn)達(dá);非線性電報(bào)方程解的存在性[J];黃金學(xué)報(bào);1999年02期

9 范恩貴,張鴻慶;非線性波動(dòng)方程的孤波解[J];物理學(xué)報(bào);1997年07期

10 王海明;非線性電報(bào)方程的周期解[J];應(yīng)用數(shù)學(xué);1997年02期

，

本文編號(hào)：2433311