B-splines for initial and boundary value problems
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Date
2013-02
Authors
Joan Yah Ru., Goh
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Due to the difficulty of solving the initial and boundary value problems analytically, a large
number of methods have been developed to approximate the solution of these problems. There
has been intere t in thi area of late and there is scope for the investigation and development of
new methods and approache . The objective of this work is the development and application
of B-spline method for the solution of initial value problems and boundary value problems.
In this work, interpolation methods based on cubic B-spline and extended cubic B-spline
were considered for solving linear two-point boundary value problems of order two. Extended
cubic B-spline is an extension of cubic B-spline possessing one additional free parameter, A
which makes the refinement of the produced curve possible. In order to create the best fit curve,
the most suitable value of A was found by minimizing the generated error. A higher order Bspline,
quartic B- pline, which has the same degree as extended cubic B-spline was also taken
into account in solving these problems. As the order is increased, there are infinitely many solutions.
However, the closest fit of the approximation curve could still be obtained with the help
of Gauss-Jordan elimination method and optimization approach which is applied on extended
cubic B-spline. These methods were tested on linear two-point boundary value problems, singular
boundary value problems and also nonlinear two-point boundary value problems. The
results showed that these methods are well approximate the exact solutions.
Description
Keywords
Differential equations , B-splines for initial , boundary value problems