Author/Authors :
Jalilian, R. Department of Mathematics - Razi University Tagh Bostan, Kermanshah, Iran , Rashidinia, J. School of Mathematics - Iran University of Science and Technology Narmak, Tehran, Iran , Farajyan, K. Department of Mathematics - College of Science - Bonab Branch, Islamic Azad University of Bonab, Iran. , Jalilian, H. School of Mathematics - Iran University of Science and Technology Narmak, Tehran, Iran
Abstract :
A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th. are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the efficiency of methods and compared with the methods in [23,32-34).
Keywords :
Two-point boundary value problem , Non-polynomial spline , Convergence analysis , Calculus of variation
