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 numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving test examples. Experimental results demonstrate thatour method is more effective for the problems where the exact solution is trigonometric orhyperbolic.