Abstract
A collocation method with di erent types of B-spline functions such as trigonometric and exponential cubic B-splinesfunctions are proposed from many researchers for studying the numerical solutions of many physical nonlinear partialdi erential equations and ordinary di erential equations. In this paper, a collocation nite di erence scheme based ontrigonometric and exponential cubic B-splines functions are investigated and applied for the numerical solution of two-pointboundary value problems. The convergence of trigonometric and exponential cubic B-splines is proved using diagonallydominant matrices. The numerical examples show that our method is very e ective and the maximum absolute error isacceptable.
Highlights
IntroductionWe consider the two boundary point value problem, given by α (x) V (x) + β (x) V (x) + γ (x) V (x) = g (x, V ) in [a, b],
We consider the two boundary point value problem, given by α (x) V (x) + β (x) V (x) + γ (x) V (x) = g (x, V ) in [a, b], (1)subject to boundary conditionsV (a) = V0, and V (b) = Vn, (2)where α (x), β (x) and γ(x) are coefficients and g (x, V ) is forcing function
We take different values of h on the interval [0, 1] and the results are generated with Mathematica using FindRoot function to solve the emerging algebraic equations
Summary
We consider the two boundary point value problem, given by α (x) V (x) + β (x) V (x) + γ (x) V (x) = g (x, V ) in [a, b],. The trigonometric cubic B-spline is studied to solve numerical solutions of various partial differential equations [16,17,18,19,20]. The exponential cubic B-spline is piecewise polynomial functions containing a free parameter and its properties are presented in [21], and is used for finding numerical solutions of various differential equations [22,23,24,25,26,27,28,29,30,31].
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