Tension Trigonometric Splines Interpolation Method for Solving a Linear Boundary Value Problem

By using the trigonometric uniform splines of order 3 with a real tension factor, a numerical method is developed for solving a linear second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots is approximated by central finite-difference method. The order of convergence of the method and the theory is illustrated by solving test examples. Experimental results demonstrate that our method is more effective for the problems where the exact solution is trigonometric or hyperbolic.