Dissertation > Excellent graduate degree dissertation topics show
Some Applications of Spline Functions in Numerical Solutions of Differential Equations
Author: ZhangShengGang
Tutor: WangRenHong
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Spline function Differential Equation Numerical Solutions Poisson function Type-2 triangulation
CLC: O241.8
Type: Master's thesis
Year: 2009
Downloads: 126
Quote: 1
Read: Download Dissertation
Abstract
|
The research of splines derives from the middle of 20 century,and its success application in the design of shape was 1960s,until its combination with CAGD.The theory of splines have been a useful tool in the field of approximation of functions,and more and more people use splines to solve the problem in application scope,for example,data process,numerical differentiation,numerical integration,Differential Equation,integral equation,numerical solution etc.In this paper,we process the problem of numerical solution of differential equation with splines.Chapter 1 introduces univariate cubic splines and multivariate splines roughly.Chapter 2 gives some applications of univariate cubic spline in numerical solutions of ordinary differential equations,summarizes some existing methods.This chapter discusses numerical methods for two-point boundary-value problems using univariate cubic spline and using cubic B-Spline to solving 2-order boundary-value problems.Chapter 3 discusses the application of uniform B-Spline in numerical of partial differential solution.By using two series of B-Spline,a numerical method for solutions of Poission equations has been presented in this chapter.And an numerical example is presented to illustrate the efficiency of the method.Similar method may be applied in other types of partial diffenential equations.
|
Related Dissertations
- Traveling Wave Solutions for Two Classes of Nonlinear Wave Equations,O175.29
- Study on Reaction-diffusion Model of Educational Innovation,G40
- Linearly polarized pulsed laser fields lithium atom Rydberg transitions population,O562
- Monotone Iterative Method of Positive Solution to Boundary Value Problem of Nonlinear Differential Equation,O175.8
- Study on a Class of Sturm-Liouville Boudary Value Problems,O175.8
- The Non-Linear Mixed Effect Models in Population Pharmacokinetics and Its Discussion Based on Stochastic Differential Equations,R911
- Image fusion method based on variational partial differential equations,TP391.41
- Study on Active Contours Integrating Global and Local Information,TP391.41
- Study on Level Set Evolution Without Reinitialization,TP391.41
- Stability Analysis of Numerical Methods for Nonlinear Delay Integro-differential Equations,O241.83
- Existence of Solutions of Boudary Value Problem for Nonlinear Fractional Functional Differential Equations,O175.8
- On the Risk Models with Tax,F812.42
- Construction of Reproducing Kernel Function in Two Hilbert Spaces and Numerical Approximation,O177.1
- Existence of periodic solution of second order impulsive differential equations,O175
- Methematical Analyses for Several Discrete Time Population Dynamic Systems,O242.1
- Differential Research and Improvement for Singularly Perturbated Boundary Value Problems under Nagumo Condition,O175.8
- Existence of Entropy Solutions for Elliptic Equations with P(X)-Growth,O175.25
- Numerical Study of HOPF Bifurcation and Dissipativity of Delay Differential Equations,O241.81
- Some Results on Second-Order Neutral Functional Differential Equations with Infinite Distributed Delay,O175
- Research on Similar Simulation of Gas Drainage Technology on Mining Face and Fire Prevention in Gobs,TD752.2
- Analysis of Interactions between Subgrade and Foundation and Superstructure of Mega Frame Core Tubular Structure of Super Tall Building,TU973.2
CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
© 2012 www.DissertationTopic.Net Mobile
|