Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.
Mungia, Maria and Bhatta, Dambaru, "Use of Cubic B-Spline in Approximating Solutions of Boundary Value Problems" (2015). Mathematical and Statistical Sciences Faculty Publications and Presentations. 74.
Applications and Applied Mathematics: An International Journal