Meshless Method Of Lines For Numerical Solutions Of Nonlinear Time Dependent Partial Differential Equations

Nagina, Bibi (2011) Meshless Method Of Lines For Numerical Solutions Of Nonlinear Time Dependent Partial Differential Equations. Doctoral thesis, Ghulam Ishaq Khan Institute Of Engineering Sciences And Technology, Swabi.

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Much of useful work being done today for numerical solution of partial differential equations involves nonlinear equations arising in different fields of science and engineering.Most widely used numerical techniques are finite differences, finite elements, spectral methods and collocation methods.However these methods face some limitations like construction of regular grid for irregular and complex geometries, slow convergence rate, stability and low accuracy. Another class of methods known as mesh free methods is expected to be superior than conventional mesh based methods in providing more accurate and stable numerical solution without any connective mesh.Meshless methods using radial basis functions are more flexible with high convergence rate.These methods provide very accurate numerical solution with low spatial resolution.The research presented in this dissertation is based on meshless method of lines using radial basis functions for numerical solutions of nonlinear time dependent partial differential equations (PDEs) namely, Generalized Kuramoto-Sivashinsky (GKS) equation, Kawahara type equations, Equal Width (EW) equation, Modified Equal Width (MEW) equation and Nonlinear Schrodinger (NLS) equation.First the spatial derivatives are discretize converting given PDE in to a system of first order ordinary differential equations (ODEs), which is then solved by classical fourth order Runge-Kutta (RK-4) scheme.Eigenvalue stability and convergence properties of the method are also discussed.Accuracy of the method is measured in terms of 2 L and error norms and conservative properties of mass, momentum and energy.The present method is used to solve various numerical examples available in the literature and results are compared with existing numerical techniques.The method shows superior accuracy, ease of implementation and efficiency of meshless method.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Equations, Meshless, Dependent, Method, Nonlinear, Lines, Solutions, Numerical, Partial
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Depositing User: Muhammad Khan Khan
Date Deposited: 28 Sep 2016 10:56
Last Modified: 28 Sep 2016 10:56

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