4758

4477

كارشناسي ارشد

رياضي كاربردي﴿آناليز عددي﴾

اصفهان:دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1388

چهارده، 138، ص :جدول ، نمودار

ص . ع به فارسي و انگليسي

رضا مختاري ، قهرمان طاهريان

دارد

18/8/1388

نبي الله گودرز وند جگيني ، مهدي تاتاري

1396/09/20

كتابنامه

رياضي

ID4477

به فارس و انگليسي : قابل رويت در نسخه ديجيتال

Numerical Solutions of KdV Equation Using Collocation and Radial Basis Functions Majid Mohseni majmohs@yahoo com April 15 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranFirst supervisor Dr Reza Mokhtari mokhtari@cc iut ac ir Second supervisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir 2000 MSC 65J15 65M99Key words KdV equation method of RBF collocation AbstractIn this thesis we present an expanded account of the numerical solutions of KdV equationusing collocation and radial basis functions based on an article by Dag et al 2007 Thisequation is a generic equation for the study of weakly nonlinear long waves It is an importantnonlinear evolution equation with numerous applications in Physics and Engineering Itsanalytical solutions have been found in special cases Hence nding the numerical solutionsof KdV equation is essential The numerical solutions of the evolution partial di erential equations can be foundby using the techniques known as the method of nite element nite di erence or nitevolume An important task in these methods is to generate a suitable mesh for the domainof problem This process especially for two or three dimensional problems is complex andtime consuming The meshfree or meshless methods try to circumvent the cumbersome issueof the mesh generation Remarkable appearance of meshless methods returns to the last decade They have beenapplied rapidly in nding numerical solutions of partial di erential equations ordinary dif ferential equations and etc One of the meshless methods is due to the pioneering e ort ofKansa who directly collocated the radial basis functions RBFs for obtaining the approxi mate solutions of the equations Because of the several advantages in comparison with thetraditional methods the Kansa s method which is known as the unsymmetric RBF collo cation method has been applied successfully to obtain numerical solutions of various typesof ordinary partial di erential equations These methods are very simple to implement be cause they are truly meshless in the sense that the collocation points need not have anyconnectivity requirement as needed in the traditional methods They are spatial dimensionindependent which is very attractive for modelling high dimensional problems They possesssuperior rate of convergence Therefore for small to moderate sized problems these methodsdo outperform traditional methods The structure of this thesis is as follows In chapter one we gather a brief history of KdVequation de nition of solitons and an introduction to numerical solution of PDEs using RBFcollocation Numerical solutions of KdV equation are obtained by using RBF collocation withthe aid of three di erent kinds of linearization in chapter two Chapter three is devoted toexplore numerical solutions of some special PDEs with the help of method of RBF collocation In chapters two and three accuracy of each scheme is tested by investigating the L2 L andRMS errors conservative property of invariant quantities propagation of solitons interactionof solitary waves and breakdown of initial conditions into a train of solitons

رضا مختاري ، قهرمان طاهريان

نبي الله گودرز وند جگيني ، مهدي تاتاري