Mathematics

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CUBIC B-SPLINE FOR SOLUTIONS OF BOUNDARY VALUE PROBLEMS
(2023-03-15) Doaa Shtayah
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