Numerical Solution Of Nonlinear Schrödinger Equations Based On B-Spline Galerkin Finite Element Method

• Main Author: Iqbal, Azhar
• Format: Thesis
• Language: English
• Published: 2020
• Subjects: QA1 Mathematics (General)
• Online Access: http://eprints.usm.my/52548/1/Pages%20from%20Azhar%20Iqbal%20Final%20Thesis%28PhD%29.pdf; http://eprints.usm.my/52548/

B-spline functions have been used as tools for generating curves and surfaces in Computer Aided Geometric Design and computer graphics. The main advantage of these functions are the properties of their local control points, where each control point is connected with a specific basis function. Every point determines the curve shape over a parameter range values where the basis function is non-zero. Because of these properties, B-spline functions can be used to produce the approximate solutions to partial differential equations (PDEs). Various numerical techniques are available to find the numerical solution of nonlinear PDEs. In recent years, the Galerkin method has gained much attention from researchers due to its ability to provide accurate and efficient numerical solutions to nonlinear problems. The choice of basis functions play a major role in the Galerkin method.