CUBIC B-SPLINE FOR SOLUTIONS OF BOUNDARY VALUE PROBLEMS
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Date
2023-03-15
Authors
Doaa Shtayah
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Abstract
Many of the mathematical models of engineering problems are expressed in terms of
Boundary Value Problems (BVP). The Finite Difference Method (FDM) is the most
modern method for solving (BVP). This is incredibly helpful in resolving challenging
issues involving typical geometrical shapes or boundaries. Another numerical method,
the B-spline method, has seen growing application in recent years in engineering research
to solve mathematical models.
The main objective of this study is to examine the effectiveness of cubic B-spline
functions in addressing boundary value problems. The derivation of linear, quadratic, and
cubic B-spline functions is covered at the start of the study. Subsequently, I use cubic Bspline
functions to solve second-order linear boundary value problems with nonhomogeneous
boundary conditions for ordinary differential equations, both in cases
where coefficients are constant and where they are variable.
Results from the examples show that the B-spline method leads to lower error rates
compared to the Finite Difference Method.
Keywords: Cubic spline, B-spline, differential equations, Boundary value problems,
Finite difference methods