A Modified Cubic B-Spline Numerical Solution of Singular Two-Point Boundary Value Problems
Singular two-point boundary value problems arise in a variety of applied mathematics and physics.It is a classical problem and many researchers have done a lot of research work on this issue.In this paper,we apply cubic B-spline to explore the numerical solutions of a class of singular two-point boundary value problems.The paper method is primarily based on the super convergence in approximating second-order derivative values at the knots by the combination of second-order derivative values of cubic B-spline.The paper proposed cubic B-spline possesses super con-vergence in approximating the first-order derivative/second-order derivative of given function and thus the approximation order of our method reaches fourth order.Some numerical experiments are provided to demonstrate the effectiveness of our method compared to the other existing methods.
Singular two-point boundary value problemnumerical solutioncubic B-splinesuper convergence
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